It is interesting to note that whale meat and whale oil are forbidden not because the whale is a forbidden fish but because the whale is a mammal that, obviously, does not have cloven hooves and does not chew the cud. (Louis Jacobs, The Jewish Religion: A Companion, p. 124)
Actually, this is not at all why whale meat and whale oil are forbidden. They are forbidden because the whale lacks fins and scales. If you were to find an evolutionary offshoot of the whale which had cloven hooves and chewed the cud (but was fully aquatic), it would not be kosher.
I recently read an absolutely fascinating book entitled "Trying Leviathan: The Nineteenth-Century New York Court Case That Put the Whale on Trial and Challenged the Order of Nature." Back in the nineteenth century, there was a court case regarding whether whale oil should be subject to the same taxation as fish oil. The question hinged upon whether or not the whale is a fish.
This was not at all a simple question to answer. There is no right or wrong answer! It wasn't a matter of people being unaware of the mammalian features of whales. Everybody agreed that whales give birth to live young and nurse them on milk. But does this mean that they should be termed "fish"?
As I discuss in the new edition of The Camel, The Hare And The Hyrax, there is no “right” or “wrong” method of classification. A system of classification has no independent reality. It is simply a means by which man measures and describes the animal kingdom, depending upon his purpose:
From a scientific standpoint, folk-biological concepts such as the generic species are woefully inadequate for capturing the evolutionary relationships of species over vast dimensions of time and space… This does not mean that folk taxonomy is more or less preferable to the inferential understanding that links and perhaps ultimately dissolves taxa into biological theories. This “commonsense” biology may just have different conditions of relevance than scientific biology: the one, providing enough built-in structural constraint and flexibility to allow individuals and cultures to maximize inductive potential relative to the widest possible range of everyday human interests in the biological world; and the other, providing new and various ways of transcending those interests in order to infer the structure of nature in itself, or at least a nature where humans are only incidental. (Scott Atran, “Folk Biology and the Anthropology of Science: Cognitive Universals and Cultural Particulars,” Behavioral and Brain Sciences 21 (1998) pp. 547-609)
The question in the nineteenth century was as to who should answer the question of whether a whale or a fish - theologians, whalers, naturalists, or the common man? This, too, had no simple answer.
In any case, the bottom line is that the Torah adopts a system of folk-taxonomy in which animals are classified according to their overall form and habitat rather than their physiology. Bats are listed with birds, and whales would certainly be rated as fish, part of the creation of the fifth day, not chayos or behemos. There is nothing "right" or "wrong" about this. But one thing is clear: whale meat and whale oil are forbidden not because the whale does not have cloven hooves and does not chew the cud, but rather because the whale is a forbidden fish.