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It is a very important skill to a good working society.
Most people aren’t
We already do. All quantifiable sciences (math, physics, chemistry, biology etc.) teach fundamental logics which need to me rationalized. All the other subjects teach rationality too.
Teaching rationality lessons at school may encourage normative behaviours that are ultimately detrimental to society as a whole - if we get kids to habitually perform cost-benefit analyses etc. then "irrational" but socially-beneficial behaviours will take less precedence.
If "we should teach rationality in school", we must be teachers. I am definitely not a teacher. This is a contradiction. Also, did you mean rationally or rationality? You spelled wrong.
Nooooooo... We should not teach our children how to think. Otherwise they will.. you know. Be able to think. (Can you hear the sarcasm dripping from my voice)