Before education by the state was mandatory, Americans were better educated and more literate. For instance, Tom Paine's booklet Common Sense was widely read in the last quarter of the 18th century.
Individual families choose the homeschooling lifestyle for a large variety of reasons.
Some families simply want to avoid public schooling. 1. rape 2. Some parents do not share the political or moral ideals of the State and its administrators. Homeschooling is an ideal way to avoid the problems that arise with conflicting ideals. There are as many methods of homeschooling as there are homeschool families.