I do not believe in "gay" rights. I do not believe in "straight" rights, either. I don't believe in "white" rights, "black" rights, "men's" rights, "women's" rights, "Jew" rights, "Catholic" rights, "Muslim" rights, "Eric Cartman" rights or "llama lover" rights.
I believe in human rights. I believe that those rights apply to everyone equally. I believe that the biggest, most blatant hypocrisy committed by many of today's governments is that there still exist marginalised groups whose human rights -- to which they are entitled by default, at birth, because they're human -- are not recognised.
Calling them "gay rights" subtly implies that gay people are different from the rest of humanity and therefore should have different rights. They aren't, and they shouldn't. Every human being deserves the same rights.