RE: Your initial statement to the effect of “Homeschooled Kids routinely kick public school kids butts, academically” is not comparing like demographics - and is merely stating that “Children from white, middle-class two-parent families with at least some college education do better academically than inner-city children from single parent unemployed welfare families”
Not necessarily. I would say that parents of home schooled kids DO NOT WANT their children mixing with a public school system that has a mix of white, middle-class two-parent families AND single parent kids whose family backgrounds are unknown.
They also do not want their kids to be EXPOSED to the VALUES (or lack of them) taught by public schools ( and that IMHO is a huge factor aside from academics. VALUES contribute a lot to a kid’s success or failure ( even with two parent households ) ).
No doubt parents have many reasons and motives behind a homeschooling decision. They are the parents and they decide whats best for the children.
But the self-selecting statistical aspect still is there.
You may well be right about values contributing to academic and career success, but to attribute those to homeschooling and implying an absence in other educational venues is again not supportable with any information.