there is a reason dolphins aren't fish

It may not be a very good reason. To quote Wikipedia:

Because the term "fish" is defined negatively, and excludes the tetrapods (i.e., the amphibians, reptiles, birds and mammals) which descend from within the same ancestry, it is paraphyletic, and is not considered a proper grouping in systematic biology. The traditional term pisces (also ichthyes) is considered a typological, but not a phylogenetic classification.

In other words, there are probably fish that are more distantly related to each other than one of them is to a dolphin (or you).