Simply having complex interests that the parent does not share is enough to do it, really. As a kid I had intense interest in physics, music, and computer programming. Fat fucking chance my parents were going to be able to even remotely coach me on all that. As it was, even my teachers didn't keep pace with my interest and I hit the library a shit ton. Granted, the internet helps a lot in the modern era, but how many points of view are kids going to get when they are only allowed to reference Conservapedia in most of these nut job households?How advanced does your child need to be to confound an adult? If your child is so advanced that he's getting ahead of the material, he'd only benefit more from homeschool curriculum which can alter to his pace.
Not saying ALL home school situations are like that You-Tube video, of course, but the bulk of them are in fact because of religious motivation. I guess its ok if white Christians are going it....?