Teiresias is kind of a cranky old fellow. But we can totally see why—even hough he's blind, he can "see" better than any of those around him. And he does not like what he sees.
He's in tune with the mind of Apollo and receives visions of the future. Teiresias is also gifted in the magic art of augury, or telling the future from the behavior of birds. You might think these are pretty awesome skills, but it probably really stinks when everybody around you is doomed to shame, death, or mutilation. It's probably especially annoying that whenever Teiresias does drop a little knowledge, people don't believe him. In Oedipus the King, Jocasta and Oedipus are both skeptical of his prophecies. Oedipus even goes so far as to accuse Teiresias of conspiring against him with Creon.
When Teiresias shambles on stage in Antigone, he once again gets accused of being a traitor. Ironically, this time it's Creon that accuses the prophet, saying that Teiresias must have been bribed:
How far good counsel is the best of goods?
True, as unwisdom is the worst of ills.
Thou art infected with that ill thyself.
I will not bandy insults with thee, seer.
And yet thou say'st my prophesies are frauds.
Prophets are all a money-getting tribe.
And kings are all a lucre-loving race.
Dost know at whom thou glancest, me thy lord?
Lord of the State and savior, thanks to me. (1050-1058)
Creon just can't accept it when Teiresias tells him that nature itself is rebelling against Creon's double sacrilege. The gods of the heavens and the earth are angered by the fact that he has kept a dead man from being rightfully buried and has entombed a living girl. Creon's obstinately rational mind can't accept Teiresias's irrational argument. The conflict between the king and the prophet echoes the conflict between Creon and Antigone. Once again we see the laws of man butting heads with the ancient laws of the gods.
When Creon refuses to give in, Teiresias drops the knowledge that Creon's own family will die as a result of his blasphemous actions. Before Creon can reply to news of this dark prophecy, Teiresias exits the stage. If the seer had stuck around he would've seen that his words do in fact move Creon. Along with the urging of the Chorus, Creon quickly runs off to try and avert oncoming tragedy. Of course, maybe Teiresias doesn't stick around because he knows how it's all going to turn out. Just like Sophocles' ancient audience, he's heard this story before.
Do you want all Teiresias all the time? Then check out Sophocles' Oedipus the King.