When you separate kids from their parents, you open up the doors to all sorts of mayhem. Lest you think that it's only public education is the sole source of this problem, think again. You would be suprised what kind of ideas are passed onto our kids as "truth" in settings like Sunday School, Boy Scouts, sports teams, youth groups, etc.
You can remove your child from Sunday School, youth groups, etc. It's quite a bit harder to remove him/her from the compulsory indoctrination (school) that takes up several hours of his day.