Cow = Beef
Pig = Pork
Sheep = Mutton
Chicken = Chicken
Fish = Fish
Why aren't there separate "meat words" for chicken and/or fish?
Cow = Beef
Pig = Pork
Sheep = Mutton
Chicken = Chicken
Fish = Fish
Why aren't there separate "meat words" for chicken and/or fish?
Why isn't there a "meat word" for chicken?
There is! The word is chicken.
Using the name of the animal from which some kind of meat comes for the meat is much more common than using a different word, so words like beef and pork are actually the exceptions, whereas chicken follows a stronger rule. Some other kinds of meat that we don't use special words for include:
I think it's worth pointing out why English has the specific terms beef, pork, mutton in the first place.
For a very long time after the Norman Conquest in C11, English was very much the language of the (Anglo-Saxon) peasants. Since their Norman overlords spoke French, if the lord of the manor wanted a particular type of meat for dinner, he'd tell his kitchen staff to prepare some boeuf, porc, mouton - being the French words for cow, pig, sheep (the live animals in both languages).
But most English-speaking kitchen staff, hunt followers, etc. wouldn't actually know much French at all. Obviously the cook would soon pick up the essential meanings of those three highlighted French words, but he'd naturally associate them with the cooked meat from the corresponding animals. By the same token, Anglo-Saxon peasants following / assisting their local overlords out hunting would always be doing so in a context where the quarry (the animals being hunted) were primarily perceived as food to be eaten, not living creatures requiring careful animal husbandry.
It may also be useful to note that even today some Americans (especially, cattle-ranchers) still use the plural term beeves instead of cows, cattle - again, because they primarily think of their herds as "meat on the hoof".
Although we have French-derived terms like poultry (domesticated fowl in general) and pullet (a young chicken), I'm guessing the reason we never derived a word for "cooked chicken" from French poulet is because chicken wasn't such a "rarefied" foodstuff. Even lowly peasants could raise and eat chickens themselves, so they'd just carry on using their familiar existing term. But they'd rarely get to eat beef, pork, mutton, or venison (from Old French venaison) so the thinking would be "special unusual new foodstuff" merits special unusual new foreign word.
As a consequence of this, English has a potentially useful distinction that most other languages don't have. Actually, I should be more assertive on that point - it's definitely a useful distinction. If it weren't useful, it wouldn't have been so widely adopted and faithfully preserved up to the present day.