Just because the Constitution for the United States doesn't mention public schools, doesn't preculde the several States from instituting them. See the Tenth Amendment.
I know it's called an opinion, but it can't be an arbitrary one.
From what I can tell, it's a matter of in loco parentis, IOW when you drop off your kids to a public school, you have tacitly assented to accepting what they do per the written policies and procedures of your local school district. You have every right to bitch about it at the school board or elect different offals who'll fire the principal, but that is your recourse.
Not everybody has the financial resources to send their kids to a private school.