Why does Oedipus insist on finding Laius's murderer?

Oedipus insists on finding Laius's murderer primarily because he believes it is his duty to save Thebes and restore order. At the beginning of the play, Thebes is afflicted by a terrible plague, which he views as a result of the unresolved crime of Laius's murder. Oedipus, as the king, sees it as his responsibility to protect his city and its citizens. He is determined to discover the culprit to lift the curse and bring healing to Thebes. His commitment to this duty highlights his role as a leader who prioritizes the welfare of his people.

The other options do not fully encapsulate his motivations. While personal suffering, glory, and vendetta could be secondary aspects of his character, the primary driving force behind his quest is his sense of obligation to Thebes and his desire to restore it to a state of harmony. This deeply ingrained sense of duty ultimately propels the narrative forward and leads to the tragic unraveling of his identity.