It's definitely arrogant. But after much experience trying to explain these things to people, I'm more and more convinced it's not just "if you just put it the right way they will understand". Sure, they will nod politely and pretend to understand, and may even do a passable job of reciting it, but once its cast in a slightly different light they are just as confused.
Much as with reading and writing, I think it takes an active imagination and a long slog of unlearning to trust logic (the "ought to" thinking that shields one from reality) and coming to terms with the race not being to the swift, etc, and that these effects can be quantified.
It's not that some people are incapable of it. Much like literal literacy has reached rates of 99.9 % in parts of the world, I'm convinced statistical literacy can too. But when your teacher is not statistically literate (which I hypothesise they are not, generally speaking), they will not pass that on to you. They will not give you examples where the race is not to the swift. They will not point out when things seem to happen within regular variation and when they seem to be due to assignable causes. They will not observe the battle against entropy in seating choices in the classroom. They will not point out potential confounders in propensity associations. They will not treat student performance as a sample from a hypothetical population. They will not grade multiple-choice questions on KL divergence, although that would be far more useful. I could go on but I think you get the point.
Yet to be clear, I'm not talking about just applying statistical techniques and tools. I'm talking about being able to follow a basic argument that rests on things like "yes I know they are a fantastic founder but startups fail 90 % of the time and so will they" or "if the ordinary variation between bus arrivals is 5–15 minutes and we have waited 20 minutes then there is something specific that put the bus we are waiting for into a different population." These are not obvious things to many people.
This is not a personal failure – it is a lack of role models and teachers. I wouldn't have considered myself statistically literate until recently, and only thanks to accidentally reading the right books. I wouldn't even have known what I was missing were it not for that!
I suspect it will take a few generations to really get it going.
If someone would donate me large amounts of money I would love to actively research this subject, come up with reliable and valid scales to measure statistical literacy, and so on. But in the meantime I can only think in my spare time and sometimes write about it online.