That makes sense now that you mention it. Centaurs are usually seen as barbaric forest creatures so it makes sense that they would eat like them.
I guess it depends a lot on how your personal centaur is. I always imagine my centaur-self being vegetarian like a horse, but also eating cupcakes and baked goods like a person. Then again my centaur-self grew up in Aekea, a town not a forest, so she's pretty sophisticated and has probably never even seen mutton before. I myself do not even know exactly what mutton it, I know its meat, but that's about all I know. I guess my centaur-self is similar.