Oedipus is the protagonist of Oedipus Rex by Sophocles, and he finds himself in the midst of some pretty serious trouble. He is the king of Thebes, but Thebes, once a prosperous place, is now dying and no one can figure out why. In an effort to fix things, Oedipus sends Creon to speak to the oracle and find out what the gods have to say about the plight of Thebes. Creon returns with the news that things will not get better for the city because it is harboring the murderer of their last king, Laius. Once the murderer is removed from the city, things will improve.
Oedipus immediately decrees that the murderer must be found out and removed, but the arrival of Teiresias creates a new conflict for Oedipus. Tieresias tells Oedipus that he is "living in disgrace" and hints that Oedipus is the murderer. Of course that does not sit very well with Oedipus, a proud and rather arrogant man. (In all fairness, none of us would like to hear such things spoken against us, either.) All of Tieresias's comments are true, but they are also rather enigmatic; in other words, if one did not already know what he meant, he would probably not be able to discern the meaning without help.
Oedipus gets angry and accuses both Creon and Teiresias of trying to usurp his throne, and in lines 467-480 he berates the blind prophet, claiming that Teiresias does not know as much as he does. He makes this boasting claim:
Come on, tell me
how you have ever given evidence
of your wise prophecy. When the Sphinx,
that singing bitch, was here, you said nothing
to set the people free. Why not? Her riddle
was not something the first man to stroll along
could solve—a prophet was required. And there
the people saw your knowledge was no use—
nothing from birds or picked up from the gods.
But then I came, Oedipus, who knew nothing.
Yet I finished her off, using my wits
rather than relying on birds. That’s the man
you want to overthrow, hoping, no doubt,
to stand up there with Creon, once he’s king.
Remember that Oedipus became king of Thebes when he solved the riddle of the Sphinx. Now he is suggesting that if Teiresias is so wise and smart, he would have been able to solve the riddle. In fact, when the people were suffering they needed a prophet, and Teiresius was nowhere to be found. Instead, Oedipus used his wits and to defeat the Sphinx rather than reading some obscure signs ("relying on birds" and their songs is one way the prophets could "read" the future) like Tieresias does.
The argument in lines 676-688 is virtually the same. Oedipus and Creon are discussing Laius's murder, and he asks Creon if Teiresius was aware of the former king's death back when it happened. He was. Oedipus wonders why, if Teiresias thinks Oedipus killed Laius, he did not say anything at the time. Creon confirms that the prophet did not ever speak Oedipus's name in connection to the murder.
Both arguments make the same case. Though Oedipus makes a valid point, it is not as conclusive as he thinks. It is true that Teiresias does neither speaks to the Sphinx to save the people nor accuses Oedipus of killing Laius. However, his silence does not mean that the prophet did not know how to outwit the Sphinx or know that Oedipus was the murderer. Not speaking about something is not the same as not knowing it. Teiresias knew the truth; he simply did not speak it.