I understood home school as only parents are the teachers of their children.
Of course, now the concept of homeschool is popularly associated with private school. In America, they have a body of association that determines materials for homeschoolers. Discipline is always necessary, whether is is from inside or outside. Most parents cannot follow certain schedule due to mainly other schedule demands, private schools are resulting preference when public schools are rejected as being too much bad influences. However, it is still necessary to differentiate private school from homeschool.
People go to private schools to get better education than what public schools can offer. Not isolation from society, which is what homeschoolers ideology tend to fall for, if it is not the ulterior motive.
Many Southern Americans do homeschool to keep their children from influenced by other "cultures". There is a danger in this kind of notion. Should the resulting child protrays a godly goodness to the society, then it is good. Though many examples have display just the opposite, a discrimination of cultures that are different, not to mention races.
I do not fancy the pop culture of homeschooling today. A decent public school has many pros. What's essential, is that the parents remain the ultimate source of a child's education, companionship and mentorship. No work or business should interfere that.