OK, what's the English name for Garfield's species? "Cat", of course. But in some contexts, "cat" can be ambiguous, because it can also refer to Simba or Shere Khan. And so, in contexts where clarity is important, we came up with another name that refers only to Garfield's species, and not to the others. And since any word from a modern language would be ambiguous, we used words from Latin, and call that species Felis sylvestris domesticus.

Similarly, the English name for Earth's single natural satellite is "the Moon". But in some contexts, "moon" can be ambiguous, because it can also refer to Ganymede or Phobos. And so, in contexts where clarity is important, we use a name that refers only to the world that Neil Armstrong set foot on, and we draw that name from Latin, and call that body Luna.

Yes, the IAU said otherwise. And that was a mistake, for the same reason it would be a mistake for biologists to insist that the only correct English name for Garfield's species was "cat".