Gell-Mann had probably been sensitized to the importance of non-commutativity. As a quantum physicist he would have been acutely aware that at the deepest level, nature disobeys the commutative law. And it’s a good thing, too. For the failure of commutativity is what makes the world the way it is. It’s why matter is solid, and why atoms don’t implode.
Specifically, early in the development of quantum mechanics, Werner Heisenberg and Paul Dirac had discovered that nature follows a curious kind of logic in which p × q ≠ q × p, where p and q represent the momentum and position of a quantum particle. Without that breakdown of the commutative law, there would be no Heisenberg uncertainty principle, atoms would collapse, and nothing would exist.
That’s why you’d better mind your p’s and q’s. And tell your kids to do the same.