Answer:
Fear for his own life is the reason that Theban King Oedipus gives for finding the murderer of Theban King Laius. The reason is strange on two counts. On the one hand, that isn't the reason that's given by the Oracle at Apollo's Shrine for the man hunt. The Oracle says that the murderer must be identified, and punished with death or exile, in order for the devastating pestilence to end in Thebes. On the other hand, the reason is ironically strange, because Oedipus in fact is the murderer.