This is a question with no definitive answer, but here are some factors that may have contributed to Coriolanus not being considered as one of Shakespeare’s "great tragedies":
- The play has few quotable lines or amusingly over-the-top passages. Its language is terse and much less poetic than Hamlet and others.
- Coriolanus has no particularly effectual foe or foil.
- Almost all of the action is centered on Coriolanus; he is either on stage (and the center of focus) or whoever is on stage is talking about him.
- Coriolanus’s persistent egotism makes him less of a sympathetic character than the protagonists in the other tragedies. He ends up a very lonely, unfulfilled, unrepentant character. (Count the number of times the word alone appears in the play.)
Although the story "Coriolanus" is tragic, it is not considered to be the same level of tragicness as the other stories, including Hamlet, Macbeth and Othello etc. The main reason for that theory is that the main character, whose nature is that he is very unattractive, overly obnoxious, immature, not flexible and stubbornly aristocratic, so it is very difficult to sympathise for him for all his faults and mistakes he created.
Due to his fierce distaste and fury against the lower classes of Rome social monarchy, he was later exiled from his native country