The main deep life impacting characteristic of standard public schools is coerced unwelcome company. You're forced by law to be around the same bullies for 5, 10, even 12 years. The natural order with organic friendships (and indeed probably since antiquity) is that those who act as a bully or jerk get ostracized. It is both justice and instructive for those who get excluded from one circle and must rethink their social approach to possible get accepted in another. It is how socialization is supposed to work.
Parents won't force their kids to continue to be around others they dislike, schools are totally ok with the violation of right OTOH (basically if you have a right of free association you also have a right of non association btw).