What are 3 arguments as to why Macbeth is a tragic hero?
Let's look to Aristotle for some basic characteristics of a tragic hero.
Characteristic #1 -- The tragic hero is of noble birth and seen as great by common people. This is true of Macbeth. He is not some common foot soldier. He is a military leader with a great big castle/house of his own complete with servants. Even King Duncan wants to come and see Macbeth and Macbeth's place. Kings don't do that for common plebeians.
Characteristic #2 -- The tragic hero has some kind of character flaw. This is often called "the tragic flaw." It makes the character more relatable because while the character is of great and noble birth, he's also flawed like the "rest of us." Macbeth's flaw is his ambition. I have ambition too, so I understand Macbeth's desire to be greater than he already is. Unfortunately for Macbeth, his ambition doesn't have an off switch. It's completely unbridled ambition. He is willing to kill to secure greater power, and he is willing to continue killing in order to keep his newly gotten power.
Characteristic #3 -- The hero's downfall is only partially his fault. This is also true of Macbeth, and it ties in with the tragic flaw. Macbeth can't help himself, because of his tragic flaw. He has unbridled ambition, which is much more dangerous than "normal" ambition. Additionally, I often think that if Lady Macbeth were not present, Macbeth might have been able to keep his ambitions in check. Unfortunately for Macbeth, his wife pushed her husband to the tipping point, and his desire for power took over from there.