Actually, it didn't.
I'm not that close to the history, but I've had a taste and some exposure to parts.
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I could list all kinds of little milestones - and there has been an active political movement intentionally building towards this. It's not a 'gay agenda' in the sense that the right-wing bigots likes to say, some sort of evil design against America and taking all kinds of 'special rights' and restricting yours. It's just an agenda for overcoming discrimination.
You can find little bits here and there that most clearly start that I'm aware of in the 1970's. In part the political organization was helped by there being a concentration of gay people in San Francisco - which not many people know started when veterans returning from WWII, disembarking in San Francisco, found a good number of them who were secretly gay stayed there forming some community. In the 1970's, we had the first openly gay elected person in California, Harvey Milk - though he was assassinated.
Various things were started - like gay pride parades, starting to have people doing what had not really ever been done before - say they're gay.
Ever hear the slogan "We're here, we're queer, get used to it"? That was a statement saying start adapting to the idea that gay people don't have to hide or go to jail.
I won't try to summarize all the cultural progress - all the firsts - first movie star, first whatever - but Bill Clinton was a small amount of help. He wanted to legalize gays in the military, but Colin Powell was more popular than he was, basically and resisted him, and they compromises on "don't ask, don't tell" which was seen as progress for gays at the time, but led to the expulsion of thousands of military members. Clinton also signed the federal defense of marriage act, with great popular support. The country wasn't ready.
Then in 2003 IIRC, the Supreme Court struck down all sodomy laws - basically 'jail the gays' laws - further 'legitimizing' gays by removing that legal stigma. While a large majority still opposed gay marriage, opposition was softening; and the Massachussets Supreme Court was the first state to strike down laws against gay marriage.
Very liberal Massachussetts reacted with a large majority opposing the ruling and supporting a movement to ban gay marriage again when they could in a couple years.
A funny thing happened on the way to that - gay marriage didn't actually hurt anyone, and they got used to it, and the poll numbers shifted towards support for gay marriage.
As of 2004, Republicans were still playing the game of putting anti-gay ballot measures on ballots to bring out Republican voters - but that was the last time it worked much.
Public opinion was just continuing to shift away from bigotry, slowly and gradually. By 2008 no major presidential candidate was for gay marriage, but they were for more equality.
Another significant milestone came when Joe Biden let slip he was for gay marriage. That Vice-President had more impact than the previous, Cheney, because it was based more on principle while Cheney's was seen as driven by having a gay daughter. Biden's action created pressure on President Obama - who was sort of pushed into switching from his anti-stance to a pro-stance. After he did, members (nearly all Democrats) in Congress followed; nearly every Democratic Senator came out for it.
Every Democratic nominess for President followed, all for it now.
This all followed a poll where public support for gay marriage topped 50% for the first time - politicians switched quickly.
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It's a decades-long effort to win over public opinion - it's just sped up a lot after public opinion going over 50% and Biden and Obama supporting it.