[GrantMoyer]

It makes sense if instead of thinking about intervals, you think about the supports of random variables[1]. Given two independent random variables, X is not indepent of itself, so supp(X) = supp(Y) does not imply supp(X * X) = supp(X * Y).

[1]: https://en.wikipedia.org/wiki/Support_(mathematics)#In_proba...