AHEM. Scientists are not the arbiters of language.
In North America, there is an indigenous animal usually called the buffalo, which is not related to the Asian and African buffalo. Therefore scientists insist on calling the NA buffalo "bison." Good for them.
Curiously, I hear much less complaint about how in North America people call elk "moose," and then call a completely different animal an elk which is not an elk but a deer.
Meanwhile, a killer whale is not a member of a whale family. It's a dolphin. Neither the sparrowhawk (falcon) or redtailed hawk (buteo) are hawks. The jackrabbit is a hare and the snowshoe hare is a rabbit.
Despite getting an enormous kick out of taxonomy, and the difference between Artiodactyla and Perrissodactyla, I use all these "wrong" names. By and large, the common name is a much more evocative name than the "correct" one. "Bison" is a species. A buffalo is the animal that thundered in great herds over the plains, the lifeblood of the Sioux, the animal the pale-face shot by the hundreds for sport as their trains rattled by. A buffalo is the spirit of the American west.
In the 19th century, we like to say, people thought whales were fish. Listening to Moby Dick, it occurred to me, that is completely wrong. People called whales "fish." They defined a "fish" as an animal that swims in the ocean, and by that definition, they were absolutely correct, a whale is a fish. It simply isn't true that they mistakenly believed whales to be fish. They understood that there were significant differences between whales and fish, like breathing air. But the medium of life in water made such demands upon creatures that the whale is, in many ways, more like a marlin or swordfish than it is like a buffalo (sorry, a bison). What happened was that the definition of what makes a fish changed, so that it no longer included whales.
Apparently, by the same standard we now use to exclude whales from the name of "fish," sharks are not fish either. Sharks are in a different order from fish, they are no closer relations than are whales. But I've never heard anyone protest that a shark is not a fish.
The notion of whales as distinct from fish is now so firmly fixed in the modern mind (and, yes, the distinction is a very good one), I don't call whales fish. But I no longer feel a need to wince listening to some old sea shanty about "chasing the whale-fish."