Being gay is a fetish.

[Esquilax]

The reason people state a blanket statement of it not being a choice is because it's one of their main defenses against the religious right. If they stated that it was a choice for many individuals (I can't determine whether how many homosexuals could choose to partake in relation with the opposite sex), the religious right could then use that information against them stating it was their choice to sin.
If there was no religious or other opposition to homosexuality, you wouldn't see people going around saying that it's not a choice.

The thing you're missing is that, for those individuals that may have a choice in the matter, the attractions they have are not a choice. They can choose whether to be with a man or a woman, but they cannot- at least as far as my experiences within the community have shown me- shut off their attraction to one or the other gender. I'm with a woman, that's my choice, but it doesn't stop me from being attracted to men, nor could I shut off that attraction either.

I don't know how it is for you, maybe it's different, but frankly, the choice you're talking about is not the relevant choice; for example, I know of many homosexuals that have indeed had sex with those of the opposite gender. Physiologically, everything works the same, and it's not like being gay means an automatic revulsion toward the opposite sex- I doubt many straight men are completely grossed out by exposed male abs, for example- but the actual attraction isn't there. You can have sex for many reasons, after all, and outright physical attraction isn't always one of them. Some of those reasons can even be very positive, depending on how one chooses to view sex.

This is a more nuanced situation than many religious people want to talk about, but if the religious want to talk about sin, they kinda first need to demonstrate there's a god to determine those; they don't get to just assume large chunks of the basis of their argument. As to your last point, that's entirely speculative on your part, but maybe you're right; if the religious right didn't see fit to demand that a class of people need to justify their existence to them, for some reason, then it's very possible that the idea of justifying their nature would never occur to the LGBTQ community. Doesn't mean the justification they've been forced to furnish under threat of persecution is just a political move.