Part of the problem is that rationality is a threat to many groups, and they have a tendency to consider rationality to be an ideology, equivocate between "ideology" and "religion", and then pretend that teaching rationality in public school constitutes an establishment of religion. People define their identity in terms of irrational belief systems tend to not like the idea of the next generation being raised to be rational.

And of course, things like the Prisoner's Dilemma show that individual rationality doesn't necessarily translate to group rationality, while the Efficient Market Hypothesis posits that the aggregate can be treated as being rational in the absence of individual rationality.

I think that one idea that should be discussed in schools is making intuitive reasoning explicit. For instance, I think that everyone engages in a version of Bayesian reasoning, but most people just have a vague, intuitive sense of it that is very buggy and susceptible to manipulation, like affirming the consequent ( if ((A -> B) and B), then that can be evidence for A, but is not proof). Unfortunately, in the cases where students do get lessons on rhetoric, the focus is often on constructing arguments that are persuasive, rather than on constructing arguments that are valid.

If you're arguing on the basis of the benefit to society, one point to bring up is that people should be able to debate issues constructively. That means articulating their thinking (and this in turn means being conscious of what that thinking is, which is often not a trivial issue), understanding what the thinking behind the opposing point of view is, how to clarify issues and identify the main issue of contention, etc.