Here is a dimly remembered note. Someone with clearer or more recent memory of linguistic patterns (@Demosthenes)? may be able to confirm or clarify. I’m not looking all of these up because precision isn’t necessary to the point, but please correct me if you can.
We have two words for a number of animals that we regard as food. The name of the animal typically comes from the Germanic side, the Anglo-Saxon roots. So we have Kuh = cow, Schwein = swine (pigs), Schaf = sheep. The word for the meat as meat comes from the French: boeuf (beef), porc (pork), mouton (mutton).
The comment, as I recall, was that it’s more refined to use a different word for the meat as meat because it enables us to separate it from the process of turning the animal into meat: one word for the barnyard or pasture, another for the kitchen and dining room.
I’m not sure what happened to chicken and fish. Maybe we didn’t need as much distinction there because it’s easier to think of the very small animals as “other.”