My son received a 610 on his math SAT at grade 7 without any training in Algebra. He is smarter than his teachers at math. We considered home schooling so that he could learn at his own pace.
The problem with your conclusion even assuming that your unscientific study were valid, is that you assume the children would have done better in public schools. Many parents choose homeschooling for children that have learning disabilities like ADD so they can have one-on-one instruction. These same children may not fare as well in the public schools.
In any case, your math and logic abilities have no connection to applying them to real life. You have made two logical errors. You have used anecdotal information to extrapolate to a population and you have not made a fair comparison. The question is Do home schooled children perform better or worse than children of equal intelligence and ability. Quiet frankly, if you were my children's math teacher I'd have them withdraw.
Again I am very skeptical of the "epidemics" of ADD. In a lot of cases I believe that bad teachers who don't want to be bothered prefer to say that the child has ADD instead of dealing with him (in the majority of cases, it is a him as boys are more boisterous). I had some experience of this, as my son was told he had ADD by one teacher and the psychologist told that the teacher should be examined. He finished school on the Dean's list and had an SAT of 1600... :-)
I would be the first one to acknowledge that this is a failing of schools... And I would work to remedy this...
But do you say that in the majority of cases the children have ADD? I don't think so...