The alternative to the parents being the authority, is that the state is, but the state has lied constantly about everything related to COVID and children so that would be far worse.
in Europe it’s mandatory to send your child to school - whether the parents want it or not.
No it's not. It's mandatory to educate them. Home schooling exists in Europe and parents who think teachers at a school are teaching children things that are wrong can do various things about it.