well, the German constitutional court thinks it does follow, indeed, and they are much smarter than I am in their argument:

https://www.bundesverfassungsgericht.de/entscheidungen/rk200...

In a nutshell, only schooling forces you to confront other beliefs in a way preparing you for life in a pluralistic society and thus schooling as such is a cornerstone in education.

private schools German flavor are okay because their curriculum has to comply and their final exams are state controlled.

So for example even if you went to some evangelical creationist belief system school, you'd have to understand and know evolution. And every student gets sex ed no matter if the parents think that's a bad idea, including contraceptives, abortion rights and all.

And likewise every student is confronted with the Hollerith machine planned systematic mass deportation and mass murder of 6 Mio Humans for having a "wrong" birth certificate, using scheduled, planned trains and scheduled, planned mass murder factories. And every student learns how that came to be and how a weak democracy was overturned into a mind control oppression state.

And that makes a _lot_ of sense.