If the general public realized how difficult it is to enforce the idea that every child must go to school and learn what is being taught there, they would not have to constantly discuss what schools should teach and how the schools should teach. If the government would make up its mind to require that every child receive a good education, it might not have to actually provide that education. It could allow parents to get that education for their children where and how they pleased, and only play the role of subsidizing the tuition of those who cannot afford to pay. The problem with government run education is not the requirement that children be educated, but that the government has decided that it should do the educating. No part of education should be run by the government. Because people are different and have diverse personalities and diverse needs, education needs to be diverse as well, with many different options. Government driven education is really just a method of making people exactly alike one another. Every government has the desire to tell students what to think and how to think it and they will do so if given the opportunity.
This is a paraphrase in modern terms of John Stuart Mill's thoughts on education taken from On Liberty published in 1859.