I'm really glad you asked this question! I recently answered a question about immigration where I tried to help the reader understand a different point of view by providing an opinion for both sides. I was surprised by the amount of positive feedback I received when that answer posted. That format helped people understand the complexity of the issue more than I expected.
Since I got such positive feedback last time, I'd like to do the same thing to answer your question. In order to help you understand the different arguments in favor of and against the constitutionality of requiring states to marry same-sex couples, I'll provide you with two viewpoints. First I'll answer your question as if I believe that the Supreme Court's decision was entirely legal and that they interpreted the constitution correctly. After that I'll present you with a counter-argument. To be clear, both sides will present an opinion that primarily addresses the legal issues.
Please don't let the length of this answer deter you from reading it. It's long, but it isn't dense. I've done my best to make it readable. Here we go:
The fourteenth amendment's guarantee of equal protection requires state governments to recognize and preform marriages for two people of the same sex.
Before I go too far, I need to explain why the fourteenth amendment and the concept of "equal protection" are so important. In order to do that, I'd like to present you with an analogy. For this analogy to work, you can't live in a Mormon-majority state. So if you actually live somewhere like Utah, let's pretend for a few moments that you actually live in Florida:
One day, a fellow Floridian - we'll call him "Fred" - notices a minivan pull in front of him suddenly. He's upset. He feels the owner of the minivan was driving recklessly. Fred follows the van and watches it pull into a parking lot for some kind of Church. He Googles the address and finds that it belongs to the Church of Jesus Christ of Latter-day Saints - minivan guy must have been a Mormon, Fred thinks to himself.
Whether fairly or unfairly, over the coming weeks it seems to Fred like people are always driving unsafely on the road leading up to the Mormon Church. Fred thinks about what his pastor has said about Mormons - aren't they a cult? - and wonders if cultish harsh penalties for tardiness are motivating its members to drive dangerously to arrive on time. Also, their parking lot is always full on Sundays, often for hours at a time. Do they ever go home? The whole thing made Fred uncomfortable.
Concerned, Fred contacted his state Senator, Senator Delford. Senator Delford agreed that the problem needed to be addressed. "But," he explained to Fred, "these types of things are tricky. You can't make laws targeting specific groups of people. Let me see what I can do." After hanging up with Fred, Senator Delford had a member of his staff do some background research on Mormons. Senator Delford was worried about the situation. His pastor had made similar comments about Mormons.
A few weeks later, Senator Delford's staff came back to him with a report. There is some initial evidence that Mormons are worse drivers, but it's far from conclusive. However, if the senator is certain about wanting to pursue the law, the staffers explain, they believe they've found a politically and legally feasible way to do it. Most Mormon chapels use the same architectural design, and that includes a fairly unique way of organizing their parking lots. There's zero evidence that this type of parking lot actually results in worse driving, but a law targeting these unique type of parking lots would effect almost no one but Mormons.
Senator Delford has his staff begin drafting a bill. It increases the fine, by a factor of 5, for any ticket issued to someone traveling to or from any location with the "Mormon" type of parking lot. The law gets some pushback from a local newspaper, but the Senator's spokesperson skillfully addresses the issue: "This bill is absolutely not about Mormons. Senator Delford has nothing but the greatest respect and love for Mormons personally. This bill is about addressing a specific traffic issue and improving the safety of our roads."
The bill passes by a wide margin. Police officers start patrolling roads surrounding Latter-day Saint chapels carefully, and fines for going 6 over, which would normally only be $129, are now $645 for members of the Church while they're traveling to and from Sacrament Meeting. The police are relentless about enforcement, and several people in your ward get tickets, often for violations that seem petty (going 3 over, not coming to a complete stop at a stop sign, and so on). Everyone is upset.
At this point, you probably want to object that this shouldn't be allowed because the first amendment provides freedom of religion. That's true, but not everyone would agree that freedom of religion is at issue here. It would be different if the new Florida law specifically prohibited something that was part of Latter-day Saint doctrine. For example, if the health department tried to stop Mormons from gathering together and taking the sacrament, that would certainly be a first amendment issue. That isn't the issue here, this is merely about transportation.
Hopefully you see a problem now. In a democracy, the majority sometimes imposes an unfair, arbitrary, or bad-faith will on minority groups. This doesn't mean that people are always explicitly motivated by bias or hate. For example, in this analogy implicit bias and misunderstanding - but not hate - impacted Florida's ability to govern both democratically and fairly simultaneously. (Hate did, however, play a role in gay marriage laws, and we'll get to that later.) The United States passed the 14th amendment to the constitution in order to address this problem of "majority tyranny." The part of that amendment applicable to our discussion here reads as follows:
No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws. (emphasis added)
That last phrase - "equal protection of the laws" - is extremely important. It was designed to protect minority groups from this type of majority tyranny. The amendment was passed in 1868 to deal with laws that were directly racist, as well as laws that were discriminatory in a round-about way. For example, many southern states passed laws like literacy tests and poll taxes and then exempted those whose grandfathers had been able to vote. These laws didn't directly call out any race, but no one doubted the real reason for their existence.
Do you see why this is relevant to your question? Your objection seems to be that the Supreme Court isn't really basing its decisions on the text of the constitution. But when the United States passed the 14th amendment, they were specifically instructing federal courts to look for and correct this type of majority tyranny. The other argument - or "opposing me," as I'll refer to him from now on - is going to try to argue that gay couples aren't protected by the fourteenth amendment because legalizing gay marriage was not the country's intent when they passed the equal protection clause. This fundamentally misunderstands how we apply the fourteenth amendment in this country.
Have you ever read a mystery novel? If the author was skilled, you probably felt confused throughout most of the story. You might have had different competing theories in your head about who might have committed the crime. However, when the truth was revealed, the best mystery stories make you say "Oh! Of course! How did I not see that before?" Suddenly it became clear, and evidence that previously seemed conflicting suddenly felt undeniable. Our country's understanding of discrimination sometimes works in the same way. Some forms of discrimination are not clear until our society's understanding changes. Some discrimination (which, again, is not always motivated by explicit hate) is so built into our culture that it takes time for us to see it. This is why we allow our understanding of the fourteenth amendment to evolve to include discrimination that wasn't immediately apparent when the fourteenth amendment was originally passed. Justice Kennedy, writing for the majority, explained this more elegantly than I can:
The nature of injustice is that we may not always see it in our own times. The generations that wrote and ratified the Bill of Rights and the Fourteenth Amendment did not presume to know the extent of freedom in all of its dimensions, and so they entrusted to future generations a charter protecting the right of all persons to enjoy liberty as we learn its meaning. When new insight reveals discord between the Constitution’s central protections and a received legal stricture, [in this context "stricture" basically means "restriction"] a claim to liberty must be addressed.
My analogy is flawed because a simple fine while you're driving, however severe, does not even remotely compare to the indignities suffered by LGBTQ+ people as a result of discriminatory laws. Gay couples are excluded from tax benefits, military notification, and the ability to start a family via adoption. This type of legal bullying has resulted in an astronomically high suicide rate for teenagers who identify as LGBTQ+. Few social scientists believe sexual orientation is a choice. That means that we are preventing an entire class from legal benefits.
One final thought: it's worth noting that the Supreme Court has almost always held that laws motivated by animus (animus means "ill will") toward a group of people nearly always automatically fail equal protection analysis. When you look at some of the rhetoric regarding laws that have limited the definition of marriage, it's easy to see that these laws have not always been pushed by people with kind intentions. In fact, the house report for the Defense of Marriage Act admitted the that the purpose was to "to express moral disapproval of homosexuality." They literally stated their animus as part of the official record! If these laws do not qualify as being motivated by animus, it's extremely difficult to see what laws possibly could.
The fourteenth amendment's guarantee of equal protection does not require state governments to perform marriages for two people of the same sex.
First of all, let's all recognize that protecting minorities from majority tyranny is a worthy and important goal. We should all work towards a world where everyone exists free from political and legal retribution. I don't believe my other's self's concerns about majority tyranny were nonsense. Such situations are dangerous to our democracy and should be avoided at all costs. Whether or not you agree that bans on gay marriage qualify as an example of this, you would have to be ignorant to claim that this type of majority tyranny never occurs at all.
However, my first objection - of several - to my other self's analysis has to be his unwavering confidence that article three courts (federal courts authorized by article three of the constitution) can rise above the human fallacies that cause majority tyranny in the first place. I'd like to extend the Florida analogy briefly:
Although the Church as a whole took no action when Florida passed its discriminatory law, one member, Todd Allan, seemed particularly upset. Todd had received three tickets totaling over a thousand dollars. He felt he was being unfairly discriminated against because of his faith. So Todd spoke to another member of the stake, Alice Carter. Sister Carter was a well known attorney in the area. Together, they decided to sue the state of Florida for violation of the fourteenth amendment.
They filed suit in the Federal Circuit Court for the Northern District of Florida. The case was randomly assigned to the Honorable Judge Thomas Matthews. Judge Matthews had grown up in Florida and completed his undergraduate work at the University of Florida. He studied at a prestigious law school before returning to Tallahassee to practice law. He was put on the bench about 16 years later. He had never lived outside the state of Florida longer than it had taken to complete law school. He was a devout baptist. The oral argument for the lawsuit was scheduled quickly. On the specified day, Judge Thomas looked down from the bench at Ms. Carter with a look of
Let's pause right there for a moment. Honestly, what kind of look do you imagine Judge Thomas - who is fictitious, by the way - gave the two Mormons alleging discrimination in his courtroom that morning? This is kind of unfair, because you were prepped - you know what position I'm arguing, and I went out of my way to highlight his differing religious affiliation. However, the point still stands. Why exactly is Judge Matthews so much more likely to see the discrimination that Senator Delford and Fred failed to see?
This isn't just a matter of federal courts missing discrimination. In some cases, giving judges wide latitude to interpret the constitution "as our understanding changes" has actually increased, rather than decreased, discrimination in federal law. The most obvious example is Dred Scott v. Sandford. In that case, the Supreme Court actually limited, without strong constitutional basis, the rights of a black man under existing law. I'm fully behind my other self's goal to eliminate majority tyranny, but I disagree with his proposed methods. Judges aren't necessarily more likely to see discrimination than citizens as a whole are. In fact, take a look at the "mystery novel" analogy again. If our understanding of discrimination is really as clear as he presents it, why can't people simply vote to change the discriminatory laws they created?
Your point about the constitution was valid. My other self was correct that the couples technically sued under the fourteenth amendment, but he was wrong to suggest that a "changing understanding" of equal protection is the only correct way to read the amendment. First of all, there is little to no evidence that the people of the United States were trying to solve all "majority tyranny" problems everywhere when they passed this amendment. They were trying to deal with a specific problem. The fourteenth amendment must be read in context. Second, if you really want to know if this decision was about the constitution, ask yourself "Would this decision have been any different had the United States dealt with racism in the 1860s using tools other than a constitutional amendment?" Of course not! The justices thought they knew what was best, and they were going to find any justification to do what they thought was right. This had nothing to do with the constitution and everything to do with 5 justices taking into their own hands power reserved for the people of the United States. The Chief Justices pointed this out in the closing paragraph of his dissent:
If you are among the many Americans—of whatever sexual orientation—who favor expanding same-sex marriage, by all means celebrate today’s decision. Celebrate the achievement of a desired goal. Celebrate the opportunity for a new expression of commitment to a partner. Celebrate the availability of new benefits. But do not celebrate the Constitution. It had nothing to do with it.
Finally, I want to validate your point about polygamy. You're more right than you know. In fact, the Chief Justice also cited that example in explaining the problem with the majority's thinking:
If not having the opportunity to marry “serves to disrespect and subordinate” gay and lesbian couples, why wouldn’t the same “imposition of this disability,” serve to disrespect and subordinate people who find fulfillment in polyamorous relationships?
I do not mean to equate marriage between same-sex couples with plural marriages in all respects. There may well be relevant differences that compel different legal analysis. But if there are, petitioners [the "petitioners" are the gay couples] have not pointed to any. When asked about a plural marital union at oral argument, petitioners asserted that a State “doesn’t have such an institution.” But that is exactly the point: the States at issue here do not have an institution of same-sex marriage, either.
Other me was correct to point out that the justices really were reading from the text of the 14th amendment (and not just pulling opinions out of thin air, as you had supposed), but he presented his method of 14th amendment interpretation as the only possible correct way to understand the phrase "equal protection of the law." His view is not supported by the historical context of the amendment's passage, and plenty of legal scholars - including the Chief Justice of the Supreme Court of the United States - disagree with his point of view.
Conclusion: There's basically nothing you can do.
So what can you do? Not much I'm afraid. Despite his lack of confidence, El-ahrairah is correct. One common nickname for the Supreme Court is "the court of last resort." Its decisions are final. Even if you somehow packed the Court with people who shared your point of view, Supreme Court justices are often reluctant to overthrow precedent, even if they disagree with it.
If you want the Court to more closely reflect your views in the future, your best bet is to select a presidential candidate who's views you believe in and help them get elected in 2016. A lot of justices are expected to retire during the next president's term.
P.S. Many readers who are informed about legal issues will recognize that I made some huge generalizations and glossed over a lot of issues. I know. First of all, I'm not a lawyer and mostly follow this kind of stuff out of my own personal interest. Second, I omitted a lot of information and legal nuance I did understand in order to make the answer readable. Finally, before anyone complains that I didn't represent their side well enough, let me remind you that these arguments were designed only to address legal issues.