Note that Melville was well aware of the reasons that "whales aren't fish", and went over those in detail, then said he was going to call them fish anyway.

The whale=fish thing is also an old joke about catholics. Back when one could not eat meat on fridays, all sorts of water-living mamals were declared to be "fish". So a new world protestant author in the 1800s is pointing a finger at oldworld religion.

I think that's perfectly fair. The same way everyone knows that chimps are monkeys, it's just brainy losers who insist they're just apes