Public schools actively fight to deny parents any role in shaping the values and goals of their children's education. Not true of all public schools. Ours encourages parental participation and visitation.
But public, private or "home school", parents are key to a child's learning.
I agree completely. Sure there are frustrating events in the public school, but a good parent who is involved will use those incidents as learning experiences. Even tasks as mundane as the school bus ride can present opportunities to teach values. The "data" component of an education is achievable in both public and private schools. The "values" component is what the parent's make it. I know a couple families who send their kids to the local Catholic school. They participate because they have to and go through all the motions. Their kids aren't all that.
Unless you refer to an unsafe or simply bad public school, a good education can be had in either public or private. Values are all about the parents.