Why does Oedipus criticize the Thebans in regard to King Laius's murder?

Creon comes back from the Oracle with the news that the plague in Thebes will be lifted when Laius's murderer is brought to justice. Oedipus, at this point, takes matters into this own hands and says he will find the murderer. He first offers leniency if the person who murdered Laius comes forward and confesses. He says that individual will get no worse a sentence than banishment from Thebes.
When nobody comes forward, Oedipus curses the Thebans because he believes someone is lying and covering up the murder. He is angry that the guilty party won't come forward despite the fact that Oedipus has offered him mercy and despite the fact that the entire population is suffering because of this crime.
Oedipus gets so angry he says he will exile and punish even one of his own family if he discovers that person is the murderer. What he doesn't realize is that he is guilty party.