I'm not a logician, I'm a mathematician. But they're close enough that I think I can help. There are a couple of ways to look at this, the easiest being the formal logical way and the set-theory way. In formal logic, we are basically saying that it's not a biconditional (they don't always exist together, which is an if and only if statement). Let's call the statement p "is a 'feminist'", and call q "is a fat and ugly wxmyn". Then p implies q, meaning that if someone is a 'feminist', then that person is a fat and ugly wxmyn. However, it is not necessarily the case that q implies p; that is, there exists a fat and ugly wxmyn who is not a 'feminist'. Thus we have if p then q but not if q then p, so not p only if q. Thus we don't have p if and only if q. Much like water implies wet, but wet doesn't necessarily imply water. In set theory, which I think is easier to understand, you have the set F of 'feminists', and the set W of fat and ugly wxmyns. Then for all f in F, f is also in W (because 'feminists' are fat, ugly wxmyn). However, if w is in W, then it is not necessarily in F, for the same reason that q implies p doesn't hold above. Thus we can say that F is a strict subset of W, i.e. F and W are not equal and W contains an element not in F. EDIT: Realized that I didn't fully answer the question. The reason for the shirt is to mark the whale as a member of F rather than simply a member of W, which is a relevant distinction due to the relationship between F and W.