Many questions have been asked in eNotes about whether the play should be considered the tragedy of Caesar or of Brutus. Shakespeare seems to be indicating--especially in the way he speaks of himself just before his death-- that it is definitely Caesar's tragedy and that his "tragic flaw" is hubris. For example:
I could be well moved, if I were as you;
If I could pray to move, prayers would move me;
But I am constant as the northern star,
Of whose true-fix'd and resting quality
There is no fellow in the firmament.
The skies are painted with unnumber'd sparks;
They are all fire and every one doth shine;
But there's but one in all doth hold his place.
So in the world, 'tis furnish'd well with men,
And men are flesh and blood, and apprehensive;
Yet in the number I do know but one.
Hubris was the flaw that the gods traditionally punished severely, and Caesar's behavior right up until the time Casca strikes the first blow seems intended to display the hubris that is Caesar's chief character trait as well as his tragic flaw. He is a truly superior man in many respects, but he makes himself unsympathetic to the audience by his egotistical utterances. We can see that he would become a terrible tyrant--comparable to Adolf Hitler in modern times--if he had absolute political power and command of all the Roman military forces.
It is significant that just before the conspirators close in, Caesar asks one of them:
Hence! Wilt thou lift up Olympus?
Olympus was the home of the gods. It would appear that Caesar's hubris goes beyond wishing to be a mere king: he would like to become a god and consort with Jupiter, Apollo, Minerva, Venus, and the others. When he asks, "Wilt thou lift up Olympus?" he is asking, in effect, "Wilt thou argue with a god or demigod like me?" As a matter of historical fact, Julius Caesar was made a god posthumously. His successor Octavius Caesar officially became a god and had to be worshiped as such throughout the empire. Most of the twelve Caesars also became gods. Since they had absolute political and military power, they were able to dictate to the senate and have themselves officially proclaimed gods, including the monster Caligula.
When Casca stabs Caesar saying, "Speak, hands, for me!" he is suggesting that if he were eloquent--which he knows he is not-- he would say something to the effect that the victim fully deserves to die because of his outrageous, insufferable and impious hubris.
In Greek tragedy hubris meant excessive pride toward or defiance of the gods, leading to nemesis, or downfall. The gods especially disapproved of hubris in mortals because it was a sign of competing with or actually threatening the gods.
In Plutarch's Life of Julius Caesar the Greek historian portrays Caesar as amazingly self-confident, arrogant, strong-willed, domineering, and egotistical throughout his life. In Shakespeare's play Marc Antony says that the conspirators did what they did because of "envy." This may be true enough--but they could also see, as Brutus did, that Caesar was a terrible threat to their freedom and their very lives.