It can also be a statement of solidarity or consolation. (“All of my friends have deserted me.” “Not all of your friends.”) And it can be a way of showing that there are other possibilities — alternative ways of being that can and do exist.
“Sneetches hate star-bellied sneetches,” is the general rule. But #notALLsneetches. The exceptions matter. Pointing them out matters.
“Sneetches hate star-bellied sneetches,” says a young sneetch, troubled that they are fated and required to live bound by the strictures of this general rule. “Not all sneetches,” is an important thing for that young sneetch to learn. It reminds them that they have a choice — that something different is possible, that something better is possible. An exception may sometimes prove the rule, but an exception can also challenge its rule.