In Oedipus Rex, what is the significance of Oedipus's slow coming into awareness of that identity?
It is Oedipus Rex's hubris, or excessive pride that leads to nemesis, as well as his ogre, or anger, which is the cause of his reluctant realization of the truth. In fact, the name Oedipus signifies "I think/know" and "swollen feet"; Oedipus finally discovers himself once he conquers this hubris as he realizes that the feet upon which he stands are the very feet of the murderer.
On the other hand, the reluctance of Oedipus to accept the truth of Tiresis also points to his wisdom and honorable search for what is really true as he keeps his vow to the people of Thebes, as well as his great character. For, in the first scene, the priest tells Oedipus, "You are not one of the immortal gods, we know" but he possesses the intellectual prowess to ameliorate Thebes's grave situation. Thus, it is significantly part of the tragic irony of this play that Oedipus seeks so hard to determine the cause of the plague when this cause is within himself.