It’s not even that we lack a way to define fish, it’s more that we lack a definition that isn’t arbitrary. One can define them as something like “vertebrates, except for all these ones that we don’t want to include”, but then there’s not really a clear reason to exclude all the amphibians and reptiles and mammals and such, other than that they don’t traditionally get called fish. Some of them even live in water, and a handful of fish can leave the water to a limited extent, so it isn’t even that.