Why do people think that dolphins were fish?

Because at a first glance, they look like big fish. It takes careful study of their lifestyle to realize they're mammal---giving birth to live young, feeding them milk like we feed our children, breathing air, not water, and being warm blooded. This classification goes the same for whales and porpoises. But some people don't realize these facts about dolphins and assume that because they're in the water, they're fish---which is a misconception. Bats, for instance, fly in the air like birds, but they are also mammals.