The United States of America isn't just a Democracy, it is a Democratic Republic.
The difference between a Democracy and a Democratic Republic is that in a Democratic Republic we live by the rule of law and then the will of the majority. This means that our laws exist to control the actions of both the people and the actions which the government takes on behalf of the people. We have a very clear hierarchy which establishes the Constitution as the highest legal authority, then Federal Laws, then the Federal Government, then State Laws, then the State Governments; and so on and so forth (with a few notable exceptions that are delegated by the constitution in certain areas).
To have a court overturn laws against gay marriage, would require Judges to find that some provision of the Constitution that guarantees or implies that homosexuals have the right to marry, then that lower law can be struck down. However, there's one big roadblock against using the equal protection clause, which essentially guarantees the human rights you're referring to, in order to declare these laws unconstitutional. And that's this:
Defense of Marriage Act, or DOMA, is the short title of a federal law of the United States passed on September 21, 1996 as Public Law No. 104-199, 110 Stat. 2419. Its provisions are codified at 1 U.S.C. § 7 and 28 U.S.C. § 1738C. The law has two effects:
1. No state (or other political subdivision within the United States) needs to treat a relationship between persons of the same sex as a marriage, even if the relationship is considered a marriage in another state.
2. The federal government defines marriage as a legal union exclusively between one man and one woman.
The bill was passed by Congress by a vote of 85-14 in the Senate and a vote of 342-67 in the House of Representatives, and was signed into law by President Bill Clinton on September 21, 1996.
The first part is simply a matter of establishing a state to state basis for determining the legality of same-sex marriage, but it's the second portion that really causes problems for Gay Marriage. Because if you're claiming that homosexuals are being denied the right to marriage because they cannot marry their partner, well, that's not true because of this law. If marriage is in fact defined as a union between a man and a woman, then then homosexuals being unable to enter this union with their partner isn't a denial of human rights, it's simply a consequence of the definition. That's precisely why Congress passed it in 1996.
Agree or disagree that it's a good law, if you want to strike down bans on gay marriage, you first have to kill that law. Congress isn't going to do it, because that move would be seen as support for gay marriage, and elected officials are supposed to represent the will of the people. The only other way to get around that hurdle, would be to declare that law unconstitutional, which is essentially what you're advocating. It may eventually happen, but it's not as black and white as you think or previous attempts to repeal DOMA would've succeeded (and they have obviously not).
A lot of it comes down to opinion. Life is not as black and white as people would like it to be. Semantics play an important role of the interpretation of law and determining the Constitutionality of particular laws. There are ways to frame the debate so that none of these laws are in defiance of human rights, because the concept of human rights is murky to begin with. In the Declaration of Independence it says:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.
This implies that the source of our human rights, is none other than our creator. Given that the majority of Americans believe in the Christian God, why would they possibly think that homosexuals being unable to marry (something they believe their god disapproves of) is a right which god bestowed upon them? I sincerely doubt that the opponents of gay marriage actually believe they're denying people fundamental human rights, they simply disagree with you on whether or not it is a human right.
I ultimately agree with you. I do think homosexuals should have the same legal rights of a married couple. But I recognize that the issue isn't nearly as black and white as you make it out to be and that the will of the majority is against us. Forcing the country to agree with your interpretations and opinions will not change the way people feel, it will only harden their hearts against it.
You like to paint a picture where if we don't repeal this act and we do respect the will of the majority that the majority will begin to abuse other minorities, et cetera. That's a slippery slope argument, but a possibility none the less. I personally doubt America is going to go back in time if our culture and society are allowed to evolve naturally (which is what I'm arguing for). And I think more than anything else you could do, the minority forcing the hand of the majority would only encourage a backlash and for those abuses to become more egregious.
Political affiliation in the USA is very comparable to the way a Pendulum works. When you swing very hard one way, that force is going to eventually come back at you. But when you're on the right side of history and the wrecking ball comes back, it doesn't hurt as much. I do think that same-sex marriage is on the right side of history, but lined up along the rest of the liberal initiatives that are being worked out, now is just not the right time. Supporters of Gay Marriage should wait til they won't have to shove quite as hard to get it through, because if not the backlash could be something very bad.