See, making a blanket statement based on one data point. Clearly the private schools don't teach Aristotelian logic because you didn't learn it.
(Tongue-in-cheek, don't take that seriously)
Its not that serious. I'm just pointing out that you're taking an absolute stance on something with the bare minimum information. And you're saying everyone else is wrong, their experiences be damned, because you're definitely right. And that doesn't logically hold water.
You can get a fantastic public school education at a lot of places. You can also get a fantastic education at private schools. On average, private schools are better, but not always. Some public schools are borderline delinquent daycares. Some public schools consistently produce some of the best and brightest. To say, "All public schools are trash" is factually incorrect.