Why aren't mammals and reptiles considered amphibians?
Some named groups are not monophyletic (see this post for definition if needed). Fishes do not represent a monophyletic group. Groups like "fishes" are completely awful to define but everyone would agree that no, humans are not fish!

Now, it is important to understand for many terms, there might have a scientific and a popular definition of the term. For example, when people talk about reptiles, they talk about turtles, snakes, lizards, squamates but they don't talk about mammals. Hence by "reptile" they don't mean "Reptilia". Have a look at the post If dinosaurs could have feathers, would they still be reptiles?).