Oy, what happened to this world...
Okay, a "right" can be exercised without hindrance or let from the government. If the government can permit you or stop you from doing something, it isn't a right. Take political speech, for example. If I want to criticize President John Doe, by and large I have the legal right to do so. In the main, the government can't give me permission to do it nor can it stop me from doing it. I can say basically anything I want about President John Doe and his policies and the government has no legal authority to stop me.
However, a "right" must not impose a burden upon others. To continue the political speech analogy, sure, I can criticize President John Doe and his policies as much as I like but nobody else is under any obligation to agree with me. They can agree with me if they want, they can disagree with me, they can ignore me altogether, whatever. Exercising my right to criticize the government does not burden anybody else.
Gay marriage fails both tests. In order to be legally married, one must obtain a license. If you have to obtain a Mother May I from the government, you can call what you're doing anything you like but it isn't a right.
Secondly, gay marriage could easily impose burdens upon others. It's no stretch to think that religious institutions (not just houses of worship but other religiously-affiliated institutions) will be legally required to recognize the marriage even though they find it religiously loathsome. And this is not to speak of the probability that they will face legal consequences if they choose not to perform same-sex ceremonies.
It is not a right. Yes yes yes, "but it's not FAIR".

No, it isn't. But it's also not a right. SCOTUS can hand down any decision it likes, popular sentiment can turn any direction, the President can "evolve" at any time. Guess what? It's
still not a right. Never will be.
EDIT- I've said my bit. I'm done with this thread now.