I'll take a crack at this.
Homeschooling has become the catch word for educating your child yourself. Most states at least "allow" for this type of education. Some states (like CA) have shown some hostility but been forced (or chose) to back down from more aggressive actions. Part of the reluctance by legislatures and regulators to directly engage has been the lack of regulation of homeschoolers and a lack of desire to join a public debate on their regulation.
If the government successfully adopts the language of homeschooling and refers to some of their own programs as "homeschooling", then you will begin to find government regulation of "homeschooling". The regulation will be written to cover government action and programs but homeschool opponents will use the language as a club on those who, up until now, they have been unable to affect directly.