"In general, people will be more trusting of the family to care for the children." This is because many people do not have patience for children, because they're more energetic and "annoying." So people use family biased ideas to help them cope with how annoying their children are. Well, if one is around a child that is not theirs (so they can't say that it is "THEIR child"), they're going to be like "Why should I have respect for an annoying child? They're not mine." So people are raised to only have patience for children that are theirs. So when they're around a child that's not theirs, due to this environment raising people to only have patience for children that are theirs, then they won't have as much patience, thus making them more abusive. So if people are educated to have patience for all children, regardless of genetic relations, then people would be trusted more to handle children that aren't theirs. Public school teachers are trained to handle children in terms of coping mechanisms and psychological patience so that they don't lose patience and become abusive. It would be better for a child to be taught by a professional teacher, than by a hillbilly, trashy homeschooling parent. In other terms, public education is better than homeschooling.
"You believe that family might brainwash the child in to being someone bad so you trust the school to do it." No, families brainwash their children into believing in the family institution. People not complaining about it destroys the road for allowing those to rebel against family. Things like "it's shameful to speak bad about one's family" or "you will be homeless if you don't obey your 'abusive' parents" destroy that road that allows society to rebel against the family.
"Most people will find it very intrusive. People do not like when the choice is done for them or their relatives on what they are going to be tought morals vise especially." Arranged marriages, forced marriages, "carrying on the last names," unreported domestic abuse, forced to marry one's rapist, family stress and drama, and enforced gender roles are all great examples on choices that are made by others (their families that they are relying on). And education can help those who want to rebel against that. Education can help people prove that forced marriages should not be accepted.