pat robertson would tell you that one of the twins had a horny molester soccer coach. but commenter bt's reply nails it:
I think something that often gets taken for granted in discussions about sexuality is this not-so-old-fashioned notion that sexuality is black or white, this or that. In truth, what Kinsey showed us (not prescriptively, mind you, but descriptively) is that sexuality is a spectrum. It is fluid. This is where the "nature AND nurture" theory finds solid ground, I think. Sexuality is less akin to, say, eye color and more akin to personality or, literally, identity.
You can't say that you CHOSE your personality, or your identity, right? You were born that way. It's part genetic, and part just how you were raised, but still very much a truth about who you are.
So, as we often see in identical twins, one might be silent and thoughtful, the other loud and outgoing. That doesn't seem strange to us.
What is sort of implied in your question (not by you, per se, but by society in general) is a burden of proof on the homosexual. We don't believe him, or we remain, as Pat said, unpersuaded - as though this is something requiring persuasion. We never ask for this type of proof from heterosexuals. Nobody is needing to be persuaded about anybody's heterosexuality (unless it's in regards to Kris Allen).
To theorize a second about why we're so uncomfortable owning up to the fluidity of sexuality, I think it has to do with the power that sex has over us. It controls us much more than we control it, and I think that makes humanity, particularly men (which is why you so rarely see any debate about lesbianism), very uneasy. And so it's much easier to just categorize it as one or the other and shove it in a drawer and leave it alone, and don't touch it!
Hope that offers some insight, from one layperson to another.
Also - just wanted to point out the fact that Pat Roberston said "homosexuals are homosexuals because of biological problems."
I've not heard any report that claims biological PROBLEMS are to blame. Biology, yes. Problems, no.
Again, that's like saying somebody is well-mannered and thoughtful due to biological complications.