The ancient hero who has a famous rivalry with his son is Oedipus, a tragic figure in Greek narratives. His story revolves around themes of fate, prophecy, and family dysfunction. Oedipus's conflict arises from a prophecy that he will kill his father and marry his mother, leading to a tragic confrontation with his son, Polyneices. This rivalry culminates in a complex exploration of destiny and moral responsibility within familial relationships.