Jewish religious schools (Yeshivas) teach critical thinking skills by studying the Talmud [1]. A number of Yeshiva students take the LSATs and skip college altogether to go directly to law school so powerful is the process of learning Talmud.
Basically Talmud is full of (often) legal arguments and stories and a lot of time is spent on thinking through/arguing edge conditions (e.g., a piece of property is found overlapping public space and private space).
The point is that college is absolutely not necessary to teach critical thinking skills and in my opinion this should be started at a much younger age.
Incidentally, I have found even graduates of Ivy League schools seem to not understand basic fundamentals. For example, in Economics, they don't seem to understand why housing is so expensive in certain cities and don't seem to have the analytical skills to understand why prices are high.