This is a good question. On the one hand, it might be easy to cast blame on Oedipus as a man of blindness and violence. He did kill his father and did marry his mother. However, if we look at Oedipus's reaction to the suffering of Thebes, a different picture emerges.
First, Oedipus is a caring man. When Thebes is in trouble (hit by a plague), he desires to help. So, he seeks to discover what must be done to rectify the situation. In fact, he is so committed that he will give it his greatest effort to solve the problem.
Second, when he discovers that there has been a murder of the former ruler of Thebes, which is also the cause of the pollution in the land, he will do all in his power to find the culprit.
The irony to all of this is that he is the one responsible. When it becomes clearer that he is the one responsible, rather than stopping his pursuit, he proceeds full throttle. When he realizes that he is the cause of the plague, he gouges out his eyes and goes into exile.
From this perspective, what makes Oedipus so tragic is that he is noble. He loves Thebes, his people, and his family. What we see is the downfall of a great man.