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.