Let me put it another way. If a tax paying citizen is paying for a quality education for his/her child(ren), these parents should qualify for a serious tax deduction to compensate for it. What they are essentially having to do is pay twice for educating the same child.
I understand your point. However, I am currently paying for the education of children that I don't have. If somebody with a child gets a "serious tax deduction" to compensate for the fact that they have decided to provide a better education for their children, why shouldn't I get a "serious tax deduction" to compensate for the fact that I don't have any children to educate?
In other words, a home-schooler is paying twice for the education of one child. I am paying once for the education of one child. The kicker is, I have no child to educate. My unfair tax burden is identical to the home-schooler's. Why shouldn't I get equal consideration?