The typical Left vs. Right political spectrum is a false dichotomy. Both the political Left and Right use force to mold people in society against their will. Donald Boudreaux analyzes this and explains a better political spectrum in chapter 2 of Everything Voluntary. But politics does not have a monopoly on false dichotomies.
Another one is in education, specifically between Public Schooling and Homeschooling. There seems to be a difference between the two camps, however, the difference is negligible. Both believe in the supremacy of forced education, in forcing children to learn things against their will. This is akin to the above. Both public schoolers and homeschoolers use force to mold their children against their will.
Just as the proper dichotomy in politics is the coercivist-voluntaryist spectrum, so to in education is the proper dichotomy schooling versus unschooling. They are polar opposites. One relies on force, the other does not. Certainly there is much more to unschooling than the mere absence of compulsory education, but such is the foundation. The libertarian, if he is to be logically consistent, must be both a voluntaryist politically and an advocate for unschooling. Not just homeschooling, or forced education at home, but unschooling, which begins with the absence of all compulsory education.