On the matter of public education: I'm going to assume you're from the west and/or live in a capitalistic society.
I believe we can both agree that monopolies are bad, yes? Fall in quality, rise in price. Assuming the state is an entity, like any other individual or company, why would it be appealing for the government to own almost every school? Wouldn't different schools competing for the same prospective students aim to improve their quality of education at a reasonable price, as opposed to everyone paying for the same schools (whether or not you attend them, go to private schools, or home school,) owned by the same entity, providing a similar service without worry of losing customers (students.)
We can compare the quality of state-owned schools to privately-owned colleges to draw a conclusion. I don't have data at hand, but, in my personal experience, my local high school was a death trap of bullies, avoiding the ghetto, and studying for the TAKS test (a state test) more than studying stuff that actually mattered. If you can't afford private education or a parent who can stay at home to teach you, you are coerced into going to the state school; it's involuntary, and students, on average, suffer. OTOH, my local college provides a phenomenal service and the professors are all marvelous; compared to high school, even my worst professors would've made good HS teachers. It's a safe environment with a lot of nice folk (excluding this weird trend of shooting up schools we're having lately.)
Thus, I believe the question becomes, "How could the average person afford private schools?" But then we must go into another topic; the quality of an individual's career. Assuming people are continuing to work for near minimum wages, state schools appear to be a must. Everything's interlinked and related, and it's a tricky subject, that of taxes. It pretty much boils down to a dependency on government due to the removal of certain liberties (for whatever reason, but I'll assume they're all a form of, "It's for your safety/own good.")