Peacocks are turkeys with big feathers!
(In reality, peacocks are rather a kind of pheasant, Phasianidae.).
They also ate swans, and in medieval Europe too, and it was the Kings' meat.
Peacock is the sacred bird of Hera/Juno, so it may be also for religious reasons.
Meat dishes included boar (wild pig), venison (deer), wild goat, mutton, lamb, kid, suckling pig, hare and dormice. Poultry dishes were of almost every known bird: chicken, geese, ostriches, cranes, pheasants, pigeons, doves, thrushes, figpeckers, and for the rich peacocks"