It seems that Sophocles knew, as Freud did, that the taboo against incest does not stem from any innate human instinct, as many have suggested, but from primal laws of human society. Iocasta would prefer that no one ever find out about the crimes that have been committed by Oedipus and her.
Oedipus says Jocasta may be worried that Oedipus is base born. What she most fears is the public unveiling of their crimes. This aversion eventually forces Oedipus to leave Corinth when he finds out about the prophesy.
It is these taboos, against incest and against parent murder, that are the main motivations behind the story of Oedipus Tyrannus. Ironically, in the play, these taboos do not prevent moral disintegration as they are intended to do, but directly bring it about.
This shows that Oedipus cannot look inside himself to find the truth, and he does not want to know the truth about himself.
It also says that the oracles must come true or he will never believe them again. The messenger says the king of Corinth has died and Oedipus is to be made king. Indeed, had King Laius and Queen Iocasta not been so afraid of the implications of the prophecy as to attempt to banish and kill their son, they likely again, Fate aside!