Why would they choose this if they don't believe it's right or if they want to "be cured", or if they are being threatened, ostricised, or picked on for it?
I don't think that persecution (unless it's on the level of losing one's life) would really deter homosexuals from blatant homosexual behavior. I've known two gay individuals in my life; one was extremely outspoken about it and another seemed to wear it like a badge. So I really don't think that persecution is any sort of deterrent. To these individuals their behavior is not a sin or a mental sickness - it's something that makes them different and thereby special and somehow gives added meaning to their lives. Maybe even attention that's not wholly unwanted.
And while I'm all for celebrating our differences and those qualities that make us unique, those differences that set us apart from God should not be cultivated. At any rate, I still think that in some cases it's a personal choice. In other cases it could stem from early childhood. And we can't discount the possibility that they were born that way either. We're all born with sinful natures, and it's our duty to strive against them to improve ourselves.