My best school memories are of vigorous guided class discussion and debate. Critical thinking and differing points of view seem to me to be tougher to replicate at home than in school.
Think about it: Two students and a teacher, taking turns reading, say, the Iliad, or Shakespeare; no bar to asking questions at any point; each participant sharing nuances of meaning and connections the other two may have missed; no archaic word left behind, unlearned; savoring particularly poignant passages; observing the nature of the characters, and comparing to persons known. Freewheeling days-long discussions. The only guide, the perceptive abilities of each reader. That's something PS's can't replicate. [and then, the beatings for wrong conclusions]
I slept through my high school daze...when I went to class at all. Booooorrrriiiing. Nunnathat in my homeschool!
I think it has to be facilitated differently. I guess I just don't see too much evidence that debate in differing points of view is encouraged in public school unless, of course, the terms of the "debate" are set within the framework of the prevailing agenda. There are just certain discussion taboos. Do you think a child would be encouraged to publicly express that homosexuality is deviant and perverse? Or that abortion is murder, other than in a very general way? Suppose he/she wanted to use a film clip from "Silent Scream" to support that view, or even the still photo of the 5 month fetus grasping the surgeon's finger, or to use the testimonies of women who were haunted by the memory of snuffing out the life inside of them? And suppose a child wants to open up a discussion in support of racial purity? Okay, so maybe he could get away with that last one as long as he wasn't white. But you get my point.
When I was in school, any one of those topics was fair game, and then some. I just use these as examples, but there are many more. The point is, free speech is not encouraged in public schools unless it is "acceptable" speech in support of "acceptable" points of view. It is pretty difficult to have objective discussions when the conclusion is predetermined.