I have long thought that a Constitutional amendment should be put forward that enshrines the right of Parents to:
1) select the education system and method for their children
2) the right to determine the belief system that the child will be raised with
3) the right to determine the associations and friends the child will maintain or distance themselves from
4) the right to determine appropriate punishment for their children so long as such punishment does not cause physical injury requiring medical treatment
That said, the real problem is not public education, but the access public education gives government into the family. This is exactly like what Orwell envisioned in 1984 where children would be indoctrinated and spy on their parents for "crimes against the state"--but this is turned up a notch because the Left believes their vision of government is religious, so it becomes an Inquisition.