The classical definition of a tragic hero is someone who is of a high birth, i.e., a king, a prince, a thane as in the Thane of Glamis, which designates Macbeth.
The tragic hero must have a flaw which topples him from his high position. This is called hubris, excessive pride, which Macbeth has. There are several factors that work against him and lead him to his downfall---his own ambition, the prophesies, and Lady Macbeth's encouragement. Ultimately it is his excessive pride that takes him over to the dark side. He makes a choice, a very bad one.
His pride is hurt when Duncan chooses his still inexperienced son, Malcolm, over him as the next leader of the Scottish people. On the surface this appears to be a poor choice when a great hero and warrior like Macbeth stands ready to step in.
Lady Macbeth attacks his pride when she attacks his manliness.
Once he kills Duncan, he is forced to keep on killing to protect himself. His pride will not let him surrender. He must fight to the end, even when he realizes he cannot win. He always knew that "...Blood will have blood, they say..."
Macbeth is a good man gone bad seduced by the intoxication of power, so yes, he is a tragic hero.
Yes, Macbeth is a tragic hero. The definition of a tragic hero is one who is victim of circumstances, despite of its role in the story.
In this case, Macbeth has lots of circumstantial issues going against him: His insecurities, those of his wife, his belief in the predictions of the three witches, and his lack of manhood to stand with courage in front of situations are the obstacles that make him grow weaker and weaker as the play progresses. Eventually, he earns the hatred and distrust of people who once loved and respected him like his killer, Macduff. This is basically what the qualities of a tragic hero are, and he displays them wonderfully.
If you go by the Aristotelian prescription, the tragic hero must be a person belonging to high rank/station. Macbeth, the most admired General of King Duncan, is one such towering personality. But Aristotle suggested that the ideal tragic protagonist, though not all good, must be generally inclined to the side of goodness. In his view, no villainous character can ever be tragic, for the overthrow of a villain can never arouse the emotions of "pity" and "fear" to achieve a "catharsis" of those and suchlike emotions. Macbeth, sometimes called a "villain-hero", does not conform to this Aristotelian requisite. Macbeth rather illustrates the paradoxicality voiced by the witches at the outset of the play: Fair is foul and foul is fair. Divided within his own self between his "vaulting ambition" and imaginative conscience, Macbeth is both"fair" and "foul"; both a saviour and a tyrant; both a poet and a murderer. Macbeth is a Renaissance protagonist who, by his own characteristic moral failing, invites his own fall. His decline from prosperity to adversity is the restoration of order and vindication of justice. Even then, Macbeth does not wholly alienate our sypathies though he goes down to defeat and death.