Even public school bureaucrats will tell you that parental involvement is critical in how a kid does in school. I think with home-schooled kids you are seeing some selection bias. Parents who home school are, by definition, *extremely* involved in their kids' education. With that kind of parental involvement, they'd probably be honor students in public school, also.

All of the homeschoolers I know made the decision with ideological reasons as the major factor. They reject the ideological orthodoxy that is in control of setting school curriculum and school policy. Again, when the federal government determines the rules for everyone, then special interests will vie for control. Though I personally disagree with my homeschooler friends in many ways (I am a non-theist), I think they tend to be pretty bright, serious, earnest people. Just misguided and with a very limited view of their own theology. :-)

But as much as I personally disagree, I think it's their business what they want to teach their kids and in the name of tolerance and non-coercion I support their right to do as they please. I also think it's wrong to force people to pay for an educational system they disagree with, as is required with a one-size-fits-all, centralized, federally mandated approach.

I think this raises another point. Whose responsibility is it to educate children? I contend it's the parent's responsibility. Even if the public school system is out there, it's still the parent's responsibility to make sure their kid is learning what they need to be successful in life.