What is “critical thinking” and how private schools do better teaching it?

There’s a difference from teaching and developing critical thinking skills.

Critical thinking skills can be encouraged, honed, and practiced throughout one’s life and starts from childhood onwards, but it’s one skill which I don’t think can be explicitly taught.

If a given student managed to avoid practicing and honing his/her critical thinking skills in and out of school in the first 17+ years of his/her life, there’s very little even a good Prof can do at that point as such a student would have fallen far behind.

Well…that is unless you want to water down the college/university stage of education to be a repeat of K-12 which would also be futile for the same reasons.