Parental control of education is an essential component of an ownership society. When parents are able to choose a school for their child, they're empowered. They've taken personal responsibility for their own child's education. Historically, parents have had the opportunity over when and where to school their children. It's only recently that the state has stepped in to claim that power.
When children are assigned by bureaucrats to a government school, parents lose this sense of ownership and responsibility. In today's society, public schools tend to be most effective in areas with high property values. Only parents who can afford to live in desirable neighborhoods or pay tuition to private schools can exert significant control over their children's education. School choice, whether through vouchers or tax credits, extends such empowerment to lower- and middle-income parents as well.