Society is made up of individuals. If you can demonstrate that individuals are irrational, then you have a better chance at claiming that the society is too. Yudkowsky wrote about the sanity waterline rather late when he had already covered a lot of other topics and I think this was intentional.

You can't just start from the assumption that society would be more rational if rationality was taught at school. You'd also need evidence that rationality can be taught to a lot of average people. I don't think such evidence exists. Whatever taken out from the curriculum might be replaced by something completely ineffective.

Of course, if changing the curriculum would make some of the smarter individuals more rational, and leave the average student with nothing, the result might still be a net positive. This argument wouldn't convince anyone professing egalitarianism however.

Individual benefits are far easier to sell than societal benefits. They're easier to imagine, examples are available, they're near rather than far, self interest is inherently motivating, and your reader won't be mindkilled by politics. If you can get the reader to accept the individual benefits, then you might be able to extrapolate a bit from there.

The title of this post is misleading, since you're not illustrating anything but asking for advice.

Your question rings alarm bells for me.

Assuming that rationality can be taught at school to everyone, is there even a connection between more rational individuals and a more rational society?

The problem I see here is that rationality is already very weakly defined for individuals and I know of no definitions in the context of society. A society can't even think (or can it?), how can it be rational?

Many decision processes of society are not based on rationality at all and I see no reason why the tried ways of winning (i.e. corruption) should be replaced by others assuming as the only change slightly more rational agents. Elections produces an average of opinions, this average may not change at all given more rational voters.

You will have to cover a lot of inference steps just to show that society as a whole will become more rational. Rationality isn't the only attribute of a "good" society and there might be ugly trade-offs. Whether a more rational society will have any "huge benefits" is just the last question in a chain that will surely be too much for a single article or a few sentences.

society is generally irrational

Do you mean that people are generally irrational, or that the people could change their relations to each other so as to better achieve their ends?

What you wrote seems to me an anthropomorphism of society.

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.