Furthermore, male “cows” (technically no such thing, they are called bulls or steer)don’t produce milk, nor do youg female cows that have not had calves (called heifers). Since these do not produce milk, are they permitted to be cooked with milk? Furthermore, according to the logic posed by the question, the question should be limited to chickens not roosters. Why meat and milk to be eaten together (even if not cooked together) or cooked together (even if not eaten) and is assur to have haana from the mixture (even if not eating it or you didn’t cook it) is a chok from the torah. We don’t know the reason.
I think the idea that “one came from the other” is someone mixing up “oso ves bno” and “basar bichalav”.