When Sophocles' Oedipus the King opens, Oedipus has sent Creon to Delphi to ask Apollo's oracle what to do about the plague that is destroying Thebes. Creon returns and declares that the plague is a result of Laius' killer still being present in the city.
Given this, Oedipus begins trying to discover who killed Laius, who was king of Thebes before Oedipus. Of course, early on in the play Oedipus does not realize that he himself is Laius' killer. When the prophet Teiresias reluctantly names Oedipus as Laius' killer, Oedipus immediately moves into a state of denial and claims that Teiresias and Creon are conspiring to overthrow him.
When Creon learns that he has been accused of treason, he defends himself against Oedipus' accusations. The ensuring argument between the two men reveals that Oedipus is acting in a stubborn and irrational way. Creon, on the other hand, gives sound reasons why he has no desire to be king instead of Oedipus. Creon gets Oedipus to admit that he is already virtually equal in power to Oedipus. Creon also argues that he enjoys all the privileges of being a king "without the fear" and declares that he has "royal power without anxiety".
Thus, in this argument, Oedipus, famous for his mental prowess in solving the riddle of the Sphinx, shows himself irrational, whereas Creon makes cogent arguments as to why he should not be suspected of treason.
Oedipus' charge of treason against Creon is harsh and relentless. His tone is emotional, and he is focused on being right.
In the play, Oedipus openly accuses Creon of conspiring with Teiresias to overthrow him. Oedipus maintains that Teiresias would not have accused him of being Laius' killer without Creon's prompting. In response, Creon asks Oedipus if he really understands the ramifications of his accusation.
For his part, Creon feels it unfair that he has been accused without cause. Meanwhile, Oedipus proclaims that he won't tolerate being called a murderer of a monarch. We can conclude that both men are equally uncompromising in their arguments. However, there is one important difference. Creon tries to reason with Oedipus, but the latter won't listen to truth. Oedipus is wholly focused on defending his power and position; he feels that his kingship is in jeopardy, and he lashes out furiously. Because his behavior is being dictated by his emotional state, Oedipus exhibits paranoia and rage. He refuses to admit the possibility that he may be Laius' killer. It is altogether too devastating a thought for him.
Despite his frustration with his brother-in-law, Creon tries to reason with Oedipus. He asserts that he has no desire for the throne; after all, the position is fraught with anxiety and responsibility. Creon even tells Oedipus to consult the Oracle about the veracity of his (Creon's) claims. Oedipus' response is that he must execute a swift counter-attack if he discovers plots against him.
For his part, Oedipus refuses to listen to reason. He will only entertain the possibility of treason against his person, not the likelihood of personal responsibility for regicide. So, we can see clearly that Oedipus is a prideful man. He is wholly occupied with maintaining control. To give the illusion of dominance, he is willing to resort to baseless accusations. He is even willing to entertain the thought of executing his brother-in-law to counteract supposed threats against him.
As for Creon, he is appalled that Oedipus thinks him a traitor. He argues from reason because it is the strongest argument he has. His innocence imbues his logic with heart-breaking clarity. However, Oedipus is impervious to this clarity because he is blinded by his strong emotions. So, through their arguments, we become cognizant of the characters of both men.