Incel isn’t something that you become.
I mean, involuntary anything isn’t really a choice. It’s right there in the name.
But the original self-professed incel was a woman, complaining that she was “unfuckable”. The term now tends to describe mostly men who feel fury at some social system that prevents them from caging a TradWife into their house, rather than the 00s era college NEET who just feels like their youth is being wasted because they aren’t getting laid.
The cliquishness might be a choice, but the condition certainly isn’t.
Celibacy is a lifestyle choice. Wanting sex and not having it, is not what I would call “involuntarily adopting a lifestyle choice”. Incel is rather, like you said, the feeling of being “unfuckable”. The problem, as I see it, is that the majority of men in this position are voluntarily “unfuckable”. They are actively being unlikeable by doing things like treating women like they they should be required to like them, which in turn, makes them “unfuckable”.
It’s a term that’s taken on some additional baggage/meaning. Originally it simply meant someone who was involuntarily celibate - wants to have sexual relationships, but doesn’t. Now it usually refers to someone adhering to a kind of peculiar set of ideologies around that (see: social value theories taken to some often ridiculous extremes; good ol’ fashioned misogyny/perhaps misanthropy; etc.).
There’s a kneejerk reaction to incels in the latter sense because so much that comes out of that is pretty awful. That and it’s often folks who engage with the latter stuff who are more inclined to identify with the term incel - most others who just fit the former definition just say they’re single.
IMO the latter usage is just more proof that we are failing and continuing to fail men, badly, in terms of community and mental health supports.