Sophocles most definitely characterizes Oedipus as arrogant in Oedipus Rex; in fact, arrogance is Oedipus's fatal tragic character flaw. We can especially see Oedipus's arrogance portrayed in his argument with the soothsayer Tiresias. When Tiresias announces that Oedipus is the murderer of the late King Laius and responsible for the city of Thebes' current plague, Oedipus accuses Tiresias of being unable to see the truth, as we see in his lines:
There is [strength in truth], but not for you. You don't have this, since you are blind in your ears and mind and eyes. (390-91)
Oedipus even has the audacity to accuse Tiresias as being a conspirator in Laius's murder. The bitter irony is that all the while that Oedipus is accusing Tiresias of being untruthful, Oedipus knows full well that he is indeed guilty of some murder, though at this point he does not know it was Laius he murdered, his own father, that he murdered. We first learn of the fact that Oedipus knows full well he is guilty of killing an innocent man when Jocasta reports that Laius was killed on his way to Delphi at a point where three crossroads meet. It's at the moment she says this that Oedipus's memory is stirred, showing us just how arrogant he was to have forgotten how he had murdered any innocent man and accused Tiresias for lying about Oedipus's guilt, regardless of if Oedipus knew at that point that it was Laius he had murdered. Had Oedipus been a more humble man, he would have never forgotten a murder he had committed and would have responded more humbly to Tiresias's prophecy that it was Laius whom Oedipus had murdered, because Oedipus would have better, more humbly understood that it certainly was a possibility, considering he had no idea whom he had killed.
Initially, Oedipus in Oedipus Rex has a commanding presence and dominates his subjects. By the end of the play, he will be revealed as a character to be pitied, his arrogance at believing that he is above the law of the land and that he can somehow escape his own fate, contributing to his downfall.
Oedipus is highly respected and feared as the "first of men" (36). As one who is "greatest in the eyes of all," (44) Oedipus promises to do whatever can be done but the first indication of his arrogance can be seen when he reveals his irritation at what Creon wants to say. In order to ensure his own glory, Oedipus is anxious for Creon to share the details of what he has learned so that he, Oedipus, can "dispel the stain;" (149) strongly believing in his own ability and although his intentions are noble he does have false courage.
The chorus urges Oedipus to listen to Tiresias, from whom he can learn the "wisest things," (299)Tiresias is trying to make Oedipus see his own failings but Oedipus's arrogance prevents it. Tiresias says: "Why do you vainly seek this?" (351) Tiresias is effectively indicating to Oedipus that he needs to look into his own soul for the truth because "you can learn nothing from me."(352) Oedipus feels that by Tiresias insulting him, he is effectively "dishonor(ing) the city" (359) and, rather than heed the words, he is offended by them because he only recognizes the hurt he feels and not the real issue. Oedipus, who at first recognized Tiresias's revered status and was happy to "listen," has descended rapidly and now insults a man he earlier praised and "who grasp(s) all things" (315) to the point of accusing Tiresias of being a part of the murder plot.
Rather than concentrating on the matter at hand, Oedipus becomes consumed with Creon's assumed plot and the thought that his "friend" would work with this "craftily-working wizard"(407) to drive Oedipus out. Creon recognizes Oedipus's arrogance when he tells Oedipus, "personalities like yours are justly painful to themselves."(704) He knows that Oedipus will not listen because it will expose Oedipus himself.
As the truth begins to reveal itself, Oedipus is quick to blame the god(s) (Zeus) who "willed me to do this." (766) The chorus also delivers a warning when it seems that the prophesy of Zeus - "O powerful one, if you are correctly called that" (931)- is being questioned. It is unthinkable and completely disrespectful to doubt the gods - especially in favor of a mortal as "faith wanders, lost." Oedipus is anxious to hear the whole story of his humble birth from the messenger and does not fear anything, even if it reveals that he is of lowly birth because "being born what I am I could never be another;" (1111) such is the elevated level of his confidence in himself; another indication of his arrogance. Even as the truth is revealed and he suffers, Oedipus still tries to control matters rather than waiting for the gods to decide what should become of him.