> That the way we teach what we teach is often more important than the what.

Partially agreed.

Whatever we teach today will be solved or obsolete tomorrow anyway. In fact, in school we learn methods that are never used in real life anyway. So the "what" is not fully the point.

It's how we teach it and what the point of it. The point of it is to teach how to learn things, how to practice, how to become experts, how to struggle with them and persevere eventually. It is not a sort of an exercise for our minds, but it is exactly an exercise for our minds. That's the point.

The "what" matters in that it is a foundation of knowledge upon which future knowledge and understanding is built.

So, I agree with the spirit of the argument but it is a bit more nuanced.