Although Oedipus was well aware of the fact that he was to kill his father, he never took into consideration that his father may not have been who it appeared to him. Oedipus fled his homeland in order to escape this destiny, yet that was to be his first tragic mistake. Though this first mistake is full of good intention, the gods would agree that a mortal can not avoid his destiny, and in trying to do so, Oedipus was quite arrogant.
Pride did not allow Oedipus to simply take the disgrace dished out by his father on the road. In killing his fellow man, Oedipus demonstrated to the gods that he had taken control over the lives of others, as only a god should have done.
In dealing with the Sphinx, Oedipus may have shown too much pride once again. Though he was thought of as a hero and made king, Oedipus knew that he would someday be the ruler of another city-state, and desire for wealth and power amongst man could be his only excuse for accepting. I think that this part of the story could have been a disguised method of denouncing the right of dictators to rule.
Now that pride has been established in Oedipus, I may tackle the real question at hand. His own tragic end was completely avoidable for Oedipus. Tiresias had no desire to speak. Laius' slave would have shied away from Oedipus for the rest of his years. The messenger would never have mentioned Oedipus' history had he not been asked.
Knowing that he was such a great man, Oedipus knew that he was beyond all blame in the death of Laius. He vows to find the killer, which, because of his pride, seems a task that he should easily do. Now enters Tiresias, a man who will not talk of what he knows in fear of the king's wrath. Knowing that the villain is not himself, even after being warned, Oedipus makes silence of the truth unbearable for Tiresias. Oedipus' reaction is quite a big mistake in that he calls a seer of the gods a liar. Oedipus must stick to his word and find the true killer, thus being even more proud.
Though he has been accused in the murder, Oedipus now decides that he must prove his innocence, and the guilt of someone else, by locating the sole witness. This last and most fateful act of pride somehow brings together the two people in the world who could prove Oedipus' guilt beyond doubt, one by mistake and the other against his will.