Knowledge of the shocking truth is what makes Teiresias the blind prophet refuse to help Theban King Oedipus. Teiresias is asked to identify the killer or killers of Theban King Laius.
Oedipus promises to punish the culprit or culprits with death or exile. He clearly values his reputation, his life, his job, and his family. And yet he'll lose all of that if Teiresias helps Oedipus. The reason lies in Oedipus being the very person whom he himself seeks. Albeit unknowingly, Oedipus is the killer of Laius, his father and his king. With the revelation of that crime will come that of another. Oedipus is married to his own mother, Theban Queen Jocasta.
The realization of the indecent truth behind the apparent royal marital bliss is something that Oedipus won't accept lightly. He has a quick temper, and speaks before he thinks. Teiresias knows his monarch very well, and therefore is reluctant to be the bearer of such news.
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Because the truth will bring nothing but pain.
Oedipus is outraged at Tiresias' prophecy. He thinks Tiresias is lying to him and was "put up" to telling him that by Creon. Oedipus is so furious with Tiresias, that in the process he pushes Tiresias into making another prophecy (more of a premonition) that Oedipus will be blind.
He does not know that the person he killed on the road from Corinth was Laius.
When Oedipus asks the blind prophet Tiresias who killed the previous king Laius, Tiresias states that he knows but wishes he didn't. Oedipus furiously accuses Tiresias of the murder of (Oedipus'own father), Laius - whom, of course Oedipus actually killed unknowingly.
Tiresias, the blind prophet in "Oedipus Rex," knows that Oedipus killed his father due to his prophetic abilities and deep understanding of fate. He has insights into the truths of Oedipus's past, which are hidden from Oedipus himself. Tiresias ultimately reveals that Oedipus's actions were foretold by the oracle, and his reluctance to disclose this information reflects the tragic nature of Oedipus's destiny.