You will NEVER hear me make an "always" argument, so your claim that "Lincoln must be a menace by [my] logic" is a strawman. There are always exceptions. Lincoln was one of the great men of history. We are all fortunate for his success, but it's not a model for education.

I have stated it before and I'll state it again: public education IS broken. But that doesn't mean we should abandon public education, because societies without public education are terrible. We need to fix what we have. Leaving it to markets is basically creating a caste system, whereby people who can afford a good education get credentialed for high status, and everyone else languishes in bad schools and lifelong poverty.