Critical thinking skills are not taught because they teach you how to question authority, and that means criticizing parents, teachers and the system. Socrates already tried doing that and was accused of corrupting youth (and got him condemned to death)
critical thinking also incentivizes discontent, generally speaking. better not to ask the difficult questions
http://classics.mit.edu/Epictetus/epicench.html
It's a short but amazing read. On can't believe it was written 2151 years ago :) Let me know if you liked it, I'm curious!