Fish are not considered amphibians because they can't live out of water. An amphibian spends part of its life in water and part on land.
Amphibians do not have scales, are cold blooded, are vertebrates and have gills for part of their lives. Some fish have scales, but they also have gills for their entire lives. Fish are also cold blooded and vertebrates. Fish breathe through their gills, whereas amphibians breathe through their skin.
Frogs, salamanders and newts are some examples of amphibians. Some examples of fish are catfish, salmon and sharks. The five groups of vertebrates are fish, amphibians, reptiles, birds and mammals.