In Shakespeare's Julius Caesar, how does Brutus justify the assassination of Caesar?
Brutus and the conspirators kill Julius Caesar because they believe he is bent on tyranny and is set to dissolve the senate (and thereby dissolve the republic of Rome). When Cassius speaks to Brutus to convince him that Caesar must be killed before he can be crowned emperor, Brutus acquiesces and compares Caesar to a serpent.
And therefore think him as a serpent's egg,
Which, hatch'd, would as his kind grow mischievous,
And kill him in the shell
The preemptive action proposed by Cassius and agreed to by Brutus and the other conspirators is meant to defend the voting power of the senate and thus protect the republic of Rome against potential tyranny from a single ruler.
In explaining the murder to the crowd, Brutus cites this political motive clearly.
If then that friend demand why Brutus rose against Caesar, this is my answer,--
Not that I loved Caesar less, but that I loved Rome more.
Had you rather Caesar were living, and die all slaves, than that Caesar were dead, to live all freemen?
Thus the murder of Caesar is justified by Brutus as a way of defending the integrity of the state. If Caesar lived, according to Brutus, then all of Rome would have been subject to the whim and the will of Caesar. The voting power of the senate would have been nullified. The people's interests then would have had no representation in the government.
What we should note is how carefully Brutus delineates the actions of the conspirators from the ambition of Caesar. Having violently deposed the leader of the senate and now standing as the next in line to leadership, Brutus is compelled to suggest that he is not ambitious. He goes to great lengths to paint Caesar as the ambitious figure and to depict himself as a humble servant of Rome.
Should we trust Brutus in his self-avowed humility?
The play lets us believe that Brutus, by and large, is a true patriot. Yet he is sly. He accepts advice from those he agrees with and rejects advice from others, thereby making himself seem open to suggestion while he may actually be simply keeping his own council. Brutus is certainly troubled by his actions and we might wonder just how best to understand his character and his motives.
In his speech to the Roman crowd after Caesar's assassination, Brutus emphasizes first that he was Caesar's dear friend, but that he had to kill him for the good of Rome. In short, he claims that his action demonstrated "not that I loved Caesar less, but that I loved Rome more." It was out of a sense of duty to the Roman Republic, which Brutus argued was under threat due to Caesar's ambition:
As Caesar loved me, I weep for him; as he was fortunate, I rejoice at it; as he was valiant, I honor him; but as he was ambitious, I slew him.
He concludes his speech by offering the citizens of Rome a stark choice, essentially arguing that had Caesar survived, he would have deprived them of their status as citizens of a free republic, and because none wanted to see that happen, Brutus says, "none have I offended." The crowd agrees with Brutus, but of course is then swayed by Antony's oration, which drew heavily on pathos.