The correct response to this question in a regular conversation or a scientific debate of course is, they are born gay. The correct response in a debate about legality or public policy should ideally be "That's an irrelevant question" or "That's none of the state's effing business". That is, from the libertarian freedom-based point of view.
Remember Colin Powell's famous interview where he endorsed Obama? He said that whenever people say "Obama is a Muslim", then the response "No he is not a Muslim" is correct, but the really correct and perfect response would be, "Why should it matter even if he is?".
I know gays are very emphatic about people recognizing that their orientation is something they were born with, not chose. And considering the narrow-mindedness of the general population towards gays, I can understand where they are coming from. Whether gayness is something you can choose or not is a valid question to be answered correctly in academic, social or even scientific debates. But it DOES NOT belong in the policy realm.
Because even if tomorrow it is somehow miraculously proven by scientists that being gay is a choice, Sec 377 was still wrong, and banning gay marriages is still wrong. What two consenting adults do is their choice, and the state has no business poking its nose into it. There should be no onus on them to prove that their sexual orientation is caused by nature and not by choice.
I understand that the whole "being gay is not a choice, but what you are born with" line is necessary to counter the slippery slope naysayers. Naysayers who say, you legalize gay sex, so why not legalize beastiality, prostitution, polygamy? To which the correct response should be, yes, we should! Prostitution should of course be legal, as long as it is being done by choice. Same with polygamy. As far as beastiality is concerned, if it is OK for me to buy an animal, then kill it, chop it into little pieces and eat it up, why should buying an animal and buggering it be such a crime?
In the end, I guess the choice argument is important in policy/legal debates dependent on whether you are arguing from an equality position or a freedom one. From the equality angle, which is where almost all gay activists seem to be coming from, I guess the "not a choice" point is central to the debate. From a freedom angle, it is at best peripheral.