Or does it? Coming out -- the process of telling other people, gay or straight, that you are not heterosexual -- is pretty clearly a choice. When I started that process, four decades ago, I anticipated that I would have some bad experiences (rejection, hostility, malignant ignorance, etc.), and did my best to prepare myself to deal with them. I was lucky: very few people reacted negatively. But when I did have bad experiences with straight people, it wasn't my choice, it was theirs.
At the risk of distracting the reader, let me suggest an analogy. Anti-choice bigots often try to confuse the issue by conflating the choice of having sexual intercourse with the choice to have a baby: if a woman has sex with a man, they claim, she should expect to get pregnant, and therefore her decision to have sex was a decision to have a baby, regardless of her actual intent -- and if she does become pregnant, she has forfeited all choice thereafter, except the choice of putting the baby up for adoption after its birth. Not all sex leads to conception, however, so choosing to have intercourse is not equivalent to choosing to have a baby. Nor is driving a car equivalent to deciding to die in a fiery collision. Nor is coming out a decision to be disowned by one's parents. Nor, for that matter, is expressing anti-gay opinions a decision to have those opinions derided, rebutted, and vilified -- bigots can usually recognize that distinction, at least!
I'd have thought that all this was obvious, but it obviously isn't, worse luck. I was disturbed by this mutation of the "Would anyone choose a 'lifestyle' ..." meme, which is obnoxious enough in its own right. If gay people (and their allies, presumably) are going to start trying to claim coming out and gay identity as non-choices, then where will we go from there? Evidently the trend is to deny any responsibility and choice in their lives at all, but in order to do that consistently they would have to exempt antigay people from responsibility and choice too, and I don't think that will happen. (Freedom and responsibility for thee, but not for me!) As I said in my own answer to the question about choice, no one knows what choice is, and the science which is used to claim that homosexuality is not a choice doesn't recognize that human beings make any choices at all, since it considers free will an illusion. But the people who claim they were born gay don't realize this: they do believe they make choices, but being gay isn't one of them... and now, it appears, coming out wasn't a choice either.
I must admit, of course, that this has to do with a blind spot of my own. To quote myself:
... unlike most gay people I’ve known, I did not expect everything to be easy when I came out. There’s a weird paradox there: most people who, like me, made a conscious move to come out to straights, seem to have delayed that move as long as we did because we feared the consequences: that our friends, our families, random strangers would hate and despise us for being queer. And yet, after coming out, a good many gay people express shock and dismay that not everyone treats them with respect, let alone acceptance. I’m deliberately echoing Captain Renault’s famous line from Casablanca: I am shocked! shocked, I tell you! to find that there is homophobia going on here. Their shock may be as theatrical, as fake, as Captain Renault's; what I don't get is what it's supposed to achieve.