Despite having agreement with rightoids, homeschooling should be illegal. If your kids have autism or some other social condition, it should be considered an extremely severe form of child abuse. I went to a special high school and there was an autistic kid there who was homeschooled for middle school to keep him away from it and it fucked him up. Even at our school he didn't really have any friends and that was an accomplishment. In order to not fit in where I went, you had to seriously work at being a jackass. There was a kid with very severe autism and he fit in better then the home schooled kid who had potential to be "passing."
I think homeschooling is an excuse to have your older children babysit the younger children all day long and that they get zero education, and I agree it probably should mostly be illegal. I will make exceptions for kids dealing with severe anxiety or something.
Kids like that would be the most harmed I think. Kids need to learn to get over their anxiety issues. Public schools harm autistic kids by creating spaces where they never have to get outside of their comfort zone. You will fail in the "real world" if you can't handle overcoming "anxiety."