Why was homeschool illegal

The U. S. Supreme Court has never ruled on homeschooling specifically, but in Wisconsin v. Yoder, 1972 it supported the rights of Amish parents to keep their children out of public schools for religious reasons.

From the government's perspective, homeschooling is kinda ambiguous. It allows at least some kids to receive a sub-par education, which is educational neglect ... So, the main reason the government might make homeschooling illegal or highly regulates is that it may lead to a poor education for their future citizens.