That is what is in dispute, isn't it. They say they want the same liberties as everyone else. You say they want to destroy marriage as an institution. My understanding is that they do not believe that the legal options already in existence are fair. Trying to prove that their real agenda is to destroy the institution of marriage will take more than hatred - it will take real evidence.
Why do you insist all disagreement with you is "hatred"?
The Overhauling of Straight America: this information, written by 2 gays, explains the gay agenda
http://www.leavethekidsalone.com/ltka_html/overhaul_2.htm
If you go and read the websites of the GLBTQ activists groups, it's all there. I don't spend my time there, have better things to do.
And WRT liberties and legal rights, it doesn't matter what they SAY they believe . . . they can say they believe anything. What matters is what is available to them as a matter of law. That's not arguable or a matter of personal opinion. The law varies somewhat from state to state, but it is clear that in this state you can set up whatever legal relationship you like between adults. My dad is a lawyer, and he helped the two ladies next door get their domestic situation regularized. It wasn't difficult. In fact, it's so easy to set up that the local activists clearly have something else in mind when they're claiming that they don't have the same rights and liberties as everybody else.