Homeschooling is a hot button issue in the culture wars. Presently, the power to educate one's child is legal in all 50 states. However, regulation of homeschooling varies from state to state. Some states give parents complete freedom to educate their child; others require strict curriculum and achievement tests.
The debate over homeschooling has found its way to the courts. The fundamental issue with homeschooling is whether parental choice is protected under the Constitution. Those in favor argue that the Constitution protects such rights and liberties. Others advance the leftwing position that the State is solely responsible for educating the child (many advanced nations outlaw homeschooling). Pro-homeschooling legal groups like HSLDA have vigorously fought on behalf of tens of thousands of families to ensure the freedom to homeschool without having to face legal threats alone.
A noticeable pattern is that many states have regulations but not the means to enforce them. Typically, this indicates that the regulations are rammed through by secular progressive politicians with pressure from teachers unions. In other words, ideology motivates the majority of these laws, which are enacted as part of a push to destroy the family and the parents' role as true educators of their children.
Sources: Education regulations and bylaws for all 50 states, Department of Education, Coalition for Responsible Home Education, Home School Legal Defense Association