With all the scientific evidence out there that homosexuality is a biological construct, and the fact that members of the LGBT community themselves say that their sexual orientation is a part of who they are, why do some still claim that it's a choice?
I wanted to answer your question on why some claim that it's a choice.
1) They simply do not believe the scientific evidence for religious reasons. If they don't believe in evidence of evolution, why would they believe evidence of homosexuality being a biological construction?
2) Some actually believe that gay people DO feel attraction towards the same sex and can't help it but still feel that it is still a choice to act on them. They see this attraction towards same sex as sort of a biological defect (like how some people are attracted to little kids, etc.), but they don't need to act on them.
3) Some gay people DO claim that it's a choice. Personally, I don't know why and I respect their opinion, but I do have a theory on why they say this. Being gay and straight are generally clear cut in terms of attraction and who you want to be with. Bisexuality is not as clear. I personally think there is a large percentage of bisexual people, and most of them never even bothered to even try to act on their same sex attractions. (Why would you? It's not that great to be gay in today's society, you still can be attracted to the opposite sex, so why bother?) The ones who do act on their same sex attractions (other than silly experiments with friends, I do not count those) usually have a "push" for them to do this: They met someone who they were extremely attracted to and maybe fell in love, they lost their trust in the opposite sex, they simply cannot find anyone in the opposite sex dating scene, or whatever. So they can "switch" to the gay side and call it a choice. Because, technically, their act of being with the same sex is a choice for bisexual people. But their feelings and attractions? Not a choice to me.