Why is "Macbeth" regarded as a tragedy?
The definition of tragedy has changed some over the years, but the basic definition is the "downfall of a great man." The "great man" element refers not to a heroic man, but to a man a political importance. Great is meant in terms of social status. Macbeth, being a general and a thane, fits that definition.
The downfall, in almost all tragedies, is the result of either a tragic mistake or a tragic flaw in that great man. This is true in the case of Macbeth as well. His tragic flaw is his ambition. He himself calls it "o'erleaping," meaning that his ambition is overpowering, it is more than it should be. This ambition leads to his tragic mistake, which is killing King Duncan. As soon as it is done, Macbeth knows that it is mistake. He is disoriented, appalled. He says that he shall "never sleep again." He knows his action was a sin, and comments on his inability to say the word "amen." It is the murder of Duncan that leads to the murder of Banquo and on down the line to Macbeth's own death at the hands of Macduff.
In addition to these details, the classical definition of tragedy says that the "great man" is neither perfectly good nor perfectly bad. The tragic hero can't be a total villain, but he he can't be a perfect angel either. This is also true of Macbeth. The fact that he hesitates against the murder of Duncan shows that he has a conscience. Shakespeare provides the character of Lady Macbeth in part to show this. She is ready at once to commit the murder; Macbeth considers the reasons why he shouldn't and tries to stop himself from doing it. This shows he has elements of good; that he even considers it in the first place, and that he goes through with it, shows that he is bad.