Jump up an abstraction layer.
Multiplication and addition are each commutative, but performing multiplication followed by addition is not the same as addition followed by multiplication (in the real numbers), so they don't commute. Said another way, the operation of composing multiplication with addition isn't commutative.
Similarly, we can perform various operations on random variables, one being expectation value and another being multiplication (or conjunction): E(X•Y) ≠ E(x)•E(y) unless x and y are independent, so E and • don't commute.
When we say "commute" we often are directly or indirectly thinking of commutative diagrams, which capture a very general which of commutativity and allows us to precisely write down all the above.
Fun fact: associativity is also just commutativity of binary operator composition.