A genuinely free society necessarily entails getting government out of education entirely. That includes ridding our nation of the federal Department of Education. Most libertarians know that and advocate it.
But a genuinely free society entails more than that. It entails getting all government — federal, state, and local — out of education. Most libertarians know that too, even if it's only on an instinctive level.
And there is the rub. Some libertarians just won't go that far. They'll call for abolishing the U.S. Department of Education but they'll back off from calling for the separation of school and state at the state and local level. They just can't bring themselves to calling for the abolition of public (i.e., government) schooling, the repeal of state compulsory-attendance laws, the abolition of school taxes, and the end of state involvement in education.