I have no greater joy than to hear that my children walk in truth. Our godly children are our reward. The Bible teaches that the parents are responsible for our children. The Bible never gives the government authority over the children. Every reference to a child's behavior is within the context of the family.
All parents are to teach their children.
There are no exceptions. We are ultimately responsible. We do not show responsibility when we send our children off every day to some school. Our failure to assume our responsibilities will result in rebellious children. There are no Biblical precedents for allowing others to teach our children.