What is the irony behind the oracle being blind and Oedipus being able to see?

Oedipus' self-inflicted blindness symbolizes his foolishness and inability to see clearly what stood before him. Famed for his commonsense and clear thinking, Oedipus has been revealed all too human. Blinding himself is his way of taking responsibility for his part in his father's death and a symbol of new found wisdom.

Ironically, the Oracle was blind but could see everything.