One likely becomes homosexual much the same way one becomes heterosexual. Scientifically, the reasons are as yet largely unknown. We know that birth order can have effects on one's chance of being homosexual. We also know that if one half of a set of twins is homosexual the other half has a far greater chance of also being homosexual. Unscientifically speaking, we listen to what people tell us. Ask a lesbian or gay person when they 'became homosexual', and they will mostly likely will give you a look of confusion, exasperation or disgust. They will perhaps respond, 'when did you choose to become heterosexual?' or 'So, you could choose to be attracted to someone of your own gender if you wanted to?'.
Even in my own limited experience, I know that I have never chosen to be attracted to specific people. There are some people I find appealing, others I don't. I can't force myself to see differently, it just is what it is. I don't know if it was nature or nuture, but either way I don't have an active choice in who I'm attracted to. It should also be noted that actions and attractions are different things. A homosexual act does not make a homosexual person. Why people choose to have sex with people they're not attracted to is often beyond me, with perhaps the only exception being when gay men or women (historically or otherwise) feel enormous societal or familial pressure to marry someone of the opposite sex.