That is easy!
It dates back to the 1066 Norman conquest of England.
Norman French became the language of the educated, wealthy ruling classes, the politicians, lawmaker, judges etc. Basically the rich.
They naturally used their French words for the meats they ate. The French names for the animals "bœuf" for cattle; "mouton" for sheep "porc" for pigs etc. Several more.
The peasantry however, who actually used their own language, Old Engish, for the animals. "Beef" was still "cow meat" etc.
Both passed down into modern English. The Old English came to represent the animals and the French the meat.
This theory has been disputed, but I've never seen any credible evidence to debunk it.
I have never found another language which displays this disparity between animal and meat.