Just like the Sequences say somewhere, putting a label "cold" on a refrigerator will not actually make it cold. Similarly, calling a lesson "critical thinking" does not do anything per se.

When I studied psychology, we had a lesson called "logic". It was completely unconnected to anything else; all I remember is drawing tables for boolean expressions "A and B", "A or B", "A implies B", "not A", and filling them with ones and zeroes. If you were able to fill the table correctly for a complex expression, you passed. It was a completely mechanical action; no one understood why the hell are we doing that; it was completely unconnected to anything else. So, I guess this kind of lesson actually didn't make anyone more "logical".

Instead we could have spent the time learning about cognitive biases, even the trivial ones, and how it applies to the specific stuff we study. For example, psychologists are prone to see "A and B" and conclude "A implies B" if it fits their prejudice. Just having one lesson that would give you dozen examples of "A and B", and you would have to write "maybe A causes B, or maybe B causes A, or maybe some unknown C causes both A and B, or maybe it's just a coincidence" would probably be more useful then the whole semester of "logic"; it could be an antidote against all that "computer games cause violence / sexism" stuff, if someone would remember the exercise.

But even when teaching cognitive biases, people are likely to apply them selectively to the stuff they want to disbelieve. I am already tired of seeing people abusing Popper this way (for example, any probabilistic hypothesis can be dismissed as "not falsifiable" and therefore "not scientific"), I don't want to give them even more ammunition.

I suspect that on some level this is an emotional decision to make -- you either truly care about what is true and what is bullshit, or you prefer to seem clever and be popular. A university lesson cannot really make you change this.