Would you break up with someone for not having sex? If so, why?

i don’t think a sexless relationship could ever work..

Ignore all the Hollywood scripts and paperback romance novels. The only reason for a man to associate with a woman is for sex. If sex isn't available, no amount of intellectual stimulation, conversation, gifts or complements are going to keep us around long term.

That depends on the situation:

If I was married or in a long term relationship where my partner for some reason was no longer able to have sex, then I would not break up with him.

If I was in a new relationship and my partner made it clear he'd never want sex, then yes, I'd break up, no matter how good that relationship was.

Sex releases chemicals that strengthen the emotional bond. Without it, unless there are specific reason, the reltionship will die. Of course that does not include out of wedlock and things like that.  You should never be forced into anything and such.  But physical touch and sex, is a corner stone of a healthy relationship.

I would because I love sex, I've already gone a year without it because of Covid (the guy I was seeing has been shielding) so have had to use my vibrator most days and I don't want to go that long again. Plus sex is an important part of a relationship and a way for a couple to show their love for each other. 

Unless your intention with having sex is to reproduce, then obviously don't have sex. So if that person doesn't want to have sex, maybe he/she doesn't want children. And you should respect that.