Well, no, what we're saying here is that if you use a rigid, hierarchical catergorisation system (cladistics) you can say that there is no such monophyletic grouping as a fish. Ie there is no grouping with a common ancestor that encompasses all the things, and only the things, that we commonly call fish. That system hasn't failed, it's fine, its purpose is to categorise things in terms of evolutionary descent. However, under that system humans are reptiles and trees and fish aren't useful categories. There exist other systems of catergorisation, which are polyphyletic or paraphyletic, which fit better with commonly used language, and we get back fish, trees, non-avian non-mammalian reptiles. Neither of them are wrong, they're just differently used and differently useful. It's like knowing that a tomato is a fruit, but nobody wants it in a fruit salad. People tend to struggle when things exist in multiple naming systems and categories for some reason.