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"Thinking out loud" has lots of interesting features, amongst which is hearing oneself say things that don't sound quite right in one's own mind. That's a good thing, not a bad one, if one keeps in mind that conversation is, like science and stories, a "work in progress." One can/should use one's own thoughts as incentive for getting things less wrong, just as one can/should use those of others.

And this does indeed seem to me to be exploring in an interesting direction, as did our class discussion that your original "thinking out loud" contributed to. No, I don't think the "private/public" school distinction is the key issue here, nor is a socio-economic distinction. And I think I agree with you that the issue is not quite "critical thinking" vs something else. That seems to me worth developing more, to see if one can get to what the real issue is. Perhaps it is in fact whether institutions of whatever kind do or do not encourage development of "thinking for yourself" (where that is not quite the same thing as "critical thinking")?

It puts me in mind of an essay I wrote shortly after coming to BMC over twenty years ago, called "This Isn't Just My Problem, Friend." Check it out, see if your thinking out loud and mine seem to you to be wrestling with related issues.