This is called “status quo bias”: we currently pay for some forms of education, defense, public safety, and fire-fighting out of taxes, therefore it must be a good idea.
Well, no. Lots of institutions exist despite not being good ideas. If this were 1950, would you be arguing “we as a society have decided that we should have Jim Crow laws”? Of course not.
Many businesses and products eventually benefit everyone. Almost everyone benefits from cars, computers, movies, dry cleaners, pizzarias. Should they socialized too?
How is a school different from a grocery store? Everybody needs them, everybody uses them. It’s inconvenient if they are too far away, or not run according to your preferences. Why aren’t grocery stores a public institution?