"Fitting in" is no small thing. The world would be better today if more people had the ability to empathize with someone not-them, sufficiently adjust their own way of interacting to put others at ease, and generally be less abrasive and fragile.
And if we want to talk in absolutes...
At best, public school provides an opportunity to learn socialization that cannot be replicated in a home environment.
The problem with this "fitting in" narrative is that as adults we don't care about it so much, people enjoy meeting new and unusual people (as long as they're baseline socially functional), there's a huge social stigma against being bigoted so basically everyone views adult bullies as worthless assholes and the cops will arrest people for much less than bullies get away with on the school yard every day even in the face of repeated parental protest.
I would say that much of adult society still runs on "fitting in" (e.g. social groups, corporate hierarchies), ergo being able to do it deftly is a huge life skill.
There's definitely a stigma around adults engaging in specific types of bullying (physical) and bigotry (e.g. protected classes), but society as a whole rewards more subtle bullying (political power dynamics) and ignores subtle bigotry (e.g. caste, microaggression).
The point of socialization, and indeed bullying itself, in school is in no small party to teach everyone (bully and bullied) what acceptable and unacceptable forms are.
Absent that, you either get people who are worse bullies (because they never learned where the line was) or are fragile (because they never learned where the "I should/shouldn't be able to handle this uncomfortable thing" line is).
And if we want to talk in absolutes...
At best, public school provides an opportunity to learn socialization that cannot be replicated in a home environment.
At worst, you get murdered.