According to Aristotle's Poetics, the tragic hero is good, though not perfect, and his fall results from his committing what Aristotle calls "an act of injustice." For Shakespeare the tragic hero has a flaw that effects his downfall; and, if this fall is to arouse in the audience emotions, it must be a fall from a height. This is why Macbeth's prowess in the battlefield is lauded and he is awarded the title Thane of Cawdor. Nevertheless, as a tragic hero, this greatness is subject to failure. In Macbeth's case, his flaw is that he is seduced by the evil sisters and their predictions because of his "vaulting ambition." Still, at first, his better nature, cautions him, still revealing some good in his character. In an aside he says,
This supernatural soliciting
cannot be ill, cannot be good. if ill,
Why hath it given me earnest of success,
Commencing in a truth? (1.3.141-144)
However, Macbeth later makes the bad judgment in considering of wondering if perhaps fate will work in his favor,
If chance will have me King, why, chance may crown me,
Without my stir. (1.3.155-156)
While he has misgivings about murdering Duncan, Macbeth makes the mistake of allowing Lady Macbeth to coerce him into killing the king. In a soliloquy Macbeth wishes to postpone this assassination, but he does recognize his "vaulting ambition which o'erleaps itself," and goes along with his wife. Perhaps, Macbeth's greatness is mitigated by his propensity to vacillate between the forces of fate, opportunity, and the influences of his wife and his own ambition. At any rate, his greatness is, indeed, flawed by and he commits an "injustice."
You might start with Aristotle's definition of a tragic hero. He specified that a tragic hero should be one of noble stature, one who has greatness about him. He must have enormous potential, someone who is admired and respected. He must also be a good man who makes a choice that causes his downfall. Shakespeare's play follows these guidelines. In order for us to feel pity and fear for our hero's fall, we must first respect his greatness.
Shakespeare establishes Macbeth's greatness from the beginning. Our first view of Macbeth displays his extraordinary courage in battle. The captain exclaims:
For brave Macbeth--well he deserves that name--(1.2)
We are given a description of how Macbeth almost singlehandedly defeated the Norweigians and won the war for Scotland. So, we immediately surmise that Macbeth is an outstanding warrior--brave, ruthless, and skillful. He is heroic.
But is he good? That is a more difficult question. He seems too easily tempted by the witches' prophecy that he will be king. He thinks of assasination very quickly. Yet, he agonizes over this action in his long soliloquy in Scene 7, reasoning that there is no justification in killing Duncan.
This inner conflict sets the stage for Macbeth's downfall, making him a tragic figure and the play a tragedy.