The first thing to point out about public education is that it involves an extreme restriction of liberty beyond anything we usually accept. How common is it for government to force you to be in a certain place at a certain time? What I call “time-place” mandates are rare. Sometimes you have to go to the DMV, but even then you spend a short amount of time there, and can generally choose when to go. Sometimes people have to respond to subpoenas or jury duty, but those are uncommon events in most people’s lives. Government says to do your taxes, though you only have a deadline and can fill out the paperwork whenever and under whatever conditions you want.
The only substantial populations of individuals who have their lives structured according to time-place mandates in a free society like ours are prisoners, members of the military, and children. The mandates for children have gotten less strict over the years now that all states allow homeschooling, but opponents of school choice for all practical purposes want to do what they can to shape the incentive structures of parents so that they all use public schools (liberal reformers tend to like vouchers that can be used at charter schools, but not ESAs, which give parents complete control). Of course, children don’t have the freedom of adults, and so others are by default in control of how they spend most of their time. But it’s usually parents, not the government, that we trust in this role. Given the unusual degree to which public education infringes on individual liberty and family autonomy, the burden of proof has to be on those in favor of maintaining such an extreme institution.