In Oedipus Rex, why is Oedipus the classic tragic hero?

Aristotle's tragic heroes must bear certain
qualities.

• A tragic hero must be a generally
  good person, worthy of esteem and possessing a measure of virtue. (If a person is bad,
  weak, or marked by vice the audience will not empathize with him/her. The ability to
  empathize with the hero is essential for effective
  tragedy.)


• A tragic hero makes a significant mistake that
  is not entirely due to his own faults. The mistake may even be made as a result of the
  character's virtues. The fact that the major mistake is not within the bounds of the
  hero's control is important. 


• The character's mistake or
  the character trait that leads to it (hamartia) is often the key to
  understanding the message of the work in which the tragic hero
  appears. 

With these criteria in mind, we can
argue that Oedipus is a tragic figure. 

Oedipus is a
strong, bold and honest man. He possesses many virtues, though he is also quick to anger
and passion. 

The major mistake made in the story is made
in an effort to be noble - Oedipus flees the possibility of fulfilling the prophecy. All
of his efforts are directed toward doing the right thing, maintaining his pride, and
avoiding the terrible predictions of the oracle. 

It is
this noble effort that leads Oedipus to marry his mother and kill his father. His
bravery and nobility cannot overcome his larger ignorance of the gods' plans. For this
reason, Oedipus cannot be directly blamed for what he has done. Clearly, he was trying
not to fulfill the prophecy. 

We can empathize with Oedipus
rather fully because he is a good person and because his mistakes were not entirely his
fault. Because he acts boldly and bravely, he fulfills the prophecy. There is no shame
in his behavior - only in its outcome.