I think this is a little unfair. For example, I know exactly what the category 'fish' contains. It contains eels and it contains flounders, without question. If someone gives me a new creature, there are things that I can do to ascertain whether it is a fish. The only question is how quickly I could do this.

We pattern-match on 'has fins', 'moves via tail', etc. because we can do that fast, and because animals with those traits are likely to share other traits like 'is billaterally symetrical' (and perhaps 'disease is more likely to be communicable from similarly shaped creatures'). But that doesn't mean the hard-and-fast 'fish' category is meaningless; there is a reason dolphins aren't fish.