Teiresias seems to hesitate to tell Oedipus the truth about his real identity because the prophet knows that it will only bring pain and upset to the king and his family. He says,

Alas, alas, what misery to be wise
When wisdom profits nothing! This old lore
I had forgotten; else I were not here.

In other words, he says that it is actually a curse to possess wisdom when that wisdom can do no good in the world. Teiresias says that, had he remembered why Oedipus might want him to come, he would not have done so. In fact, he seems to try to protect the king, saying, "'twere best / That thou shouldst bear thy burden and I mine." He speaks of the misery that his knowledge would cause Oedipus, and even though Oedipus begins to insult and rail against him, Teiresias tries to hold his tongue.

When Teiresias finally does give in and tell Oedipus that he is the "accursed polluter of this land" and that he "livest with [his] nearest kin / In infamy, unwitting in thy shame," Oedipus will not believe him. Essentially, the man Oedipus called to the palace has actually told him the truth—the very thing he claimed most to want—and, ironically, Oedipus will not believe him! Oedipus is so proud that he accuses Teiresias of having no real power and plotting with Creon, Oedipus's own trusted brother-in-law (and uncle, though he does not know this yet). Thus, Oedipus response to Teiresias helps to showcase his tragic flaw.

The blind prophet Tiresias speaks truth to power. He's generally a fearless soul who always tells it like it is, irrespective of the consequences. And he eventually does so in relation to Oedipus; but not without some slight hesitation. After all, Oedipus is king, a very powerful man who can have anyone killed at the drop of a hat. We can therefore understand Tiresias's reluctance to spill the beans straight away. He has every reason to believe that this prophecy could be his last.

It's interesting that Tiresias only reveals the terrible truth about what happened to Oedipus's father after Oedipus accuses him of murdering Laius himself. Deeply offended by the very suggestion, Tiresias finally reveals the truth, not least because he now has to defend his reputation for truthfulness and integrity from Oedipus's false accusations.

Oedipus is king, and has already in his life killed at least one man due to his pride and temper. Would you want to tell such an angry, powerful man that he has committed extreme sin? That he killed his own father? That he is responsible for the plague?Teiresias hesitates for a blend of humane and practical reasons: Who would want to give such news? And what about the consequences?That Oedipus slowly comes to an awareness of this truth on his own blends dramatic impact (it makes a better play) with spiritual/psychological realities: it takes a long time to accept difficult truths.