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StrayTom I should probably read more into the psychology of just why people think so, but it seems entirely clear even without the voluminous research into it that "nature vs. nurture" isn't one or the other.
First of all, almost everything is affected by genetics, but not because there's a "gene for gay". No, but there's probably one gene that makes your face a little more feminine, another gene which makes your voice just a little bit higher (And I'm making up this as well as the psychology for illustrative purposes, which are way too simplified) with the end result that, perhaps, most women don't find you as attractive as the guy next door.
That's where nurture enters into play, maybe there's someguy with similar genes next door, and maybe you don't have an religiously repressive father, or maybe you do but other life-experiences have taught you to rebel against him. Bearing in mind that in adulthood, people usually DON'T change their sexual orientation just because they got rejected. But sometimes, for whatever reason, people do and they might have been quite happy in their previous orientation. (Also, you said "sexuality" so I'm including fetishes etc. too which is perhaps easier to imagine).
And that longish example should also illustrate that "determine" is the entirely wrong word to use...