Here's the thing: all these identities are historically invented, culturally defined and temporary. One hundred years ago, nobody was homosexual or heterosexual. At the end of the 19th century, historian George Chauncey tells us, the identity dividing line was which sex you appeared to be, rather than which sex was the object of your desire. Girly boys were queer; butch boys were not, even if they took some sailor down to the docks. All these things get categorized differently based on your culture and era. Recently, the traditional hijra in India, Nepal, and Pakistan (born male, identify as female, attracted to men) have won legal fights to have their own third-sex box to check on identity forms (M, F, H). Would they call themselves gay or straight? No.More problematic than the "it's not a choice" position is the idea that sexual orientations are genetic in origin (as exemplified by the sweet but wrong-headed website "Born This Way" which falsely equates stereotypical cross-gendering behaviour in kids with technically defined sexual preference in adults). Even believing one's preference is not a choice doesn't necessitate the spurious scientism of genetic determinism (what's your favourite food? what's your least favourite? do you think those preferences are genetic? no? so if it was made illegal tomorrow to prefer your favourite food to your least favourite you'd just be able to stop preferring that way, right? hah). The motivation for seeking such an explanation (what Graham Chapman called "medicine's weird quest for a cause for homosexuality") is also baffling. What's to be gained? Why do you need a compelling scientific explanation for your orientation? Is it to persuade those people, the ones who hate you because they were told to by their giant invisible friend?
Human sexuality—and human identity in general—is highly complicated, far more so than any taxonomy can take into account. Language is such a limited medium for lived experience. We all choose our identities out of our culture's current list of options, but that doesn't make the identity real.
Insisting sexual orientation isn't a choice is tantamount to acknowledging the preference is wrong but you can't be judged for it because you just can't help it, whereas the better response to bigots, whether inspired by self-serving interpretations of incoherent ancient fairy tales or simple stupidity, would be "Fuck yeah, it's a choice. I chose, and I'm entitled to choose, because it's my choice to make and no-one else's and there's nothing wrong with the choice I made."
Of course, that's easy for a dyed-in-the-wool heterosexual like me to say. Not that I expect a gold star from God for avoiding behaviour that doesn't remotely appeal to me anyway, as prayhards seem to. Hell, if it's that easy to be holy, just wait a sec while I found a religion where it's a sin to eat brussels sprouts.