The predisposition to same-sex attraction is probably at least in part genetic, along with some element of socialization, any activity that could affect hormone levels, etc.
But, to act upon those attractions is not genetic at all. People also have the ability to not engage in a sex act or to enter into a certain relationship. So if we take homosexuality to be an act rather than an attraction (the word 'homosexuality' may be ambiguous in this respect, though I haven't met many celibate people who experience same-sex attraction who call themselves homosexuals so I am taking it to imply that one has engaged in said acts and is not celibate), then it must be a choice as long as we accept that we have the ability to make choices, ie. free will. If we have no free will then this is all a moot point anyway, so I'd consider "lifestyle choice" to be a more representative reflection of my view than "genetic" but that I'd rather select "Both" if I could.
Breathing and eating should also be classified as "lifestyle choices" then.