In Shakespeare's Julius Caesar, Brutus appeals to the reason of the Roman crowd. He offers himself over to their judgement, and presents them with a rational argument.
He begins by establishing that he was as much of and even more of a friend of Caesar's as any one present:
there be any in this assembly, any dear friend of
Caesar's, to him I say that Brutus' love to Caesar was
no less than his. 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. (Act 3.2.17-22)
The implication is that if Brutus loved Caesar this much, he must have had good reason for assassinating him.
This is a powerful opening, but at this point Brutus makes his mistake. He tells the crowd that Caesar was ambitious, that had Caesar lived they would have all been slaves. Everything else he says comes down to Caesar's ambition. But his mistake is that he doesn't prove Caesar was ambitious. He tells the crowd his conclusion about Caesar's character, but he doesn't prove it.
In his speech that follows, Antony proves Caesar wasn't ambitious, and thus turns the crowd into a mob.
You can find this speech in Act III, Scene 2 of the play. The basic reason that Brutus has for having conspired to kill Caesar is that Caesar was going to take too much power for himself. Brutus believes he was going to establish himself as king.
For this reason, Brutus says Rome needed Caesar dead. He says he loved Caesar, but loved Rome more. He says that the Romans had a choice -- they could have Caesar alive, but then they would be his slaves. Or they could have Caesar dead, but they would be free.