QI said (roll podcast title) There is no such thing as a fish, since that group is unbelievably diverse.

Strange that birds are dinosaurs, while Pterosaurs are not. Where is the bipedal fish that looks like a reptile or mamal, but is secretely a fish, too?

I think it's not about diversity, but lineage. The phenotype for "fish" is so tight and well defined; a salmon is closer related to a human in the tree of life than to a coelacanth even though both are categorised as "fish".