How does Cassius persuade Brutus against Caesar in Julius Caesar?

Cassius persuades Brutus against Caesar because he convinces Brutus of Caesar's tyrannical characteristics and his desire for absolute power.

When Caesar returns to Rome, having already defeated Pompey, he moves before the crowds, who want to crown him. He is offered a laurel three times, and is loath to refuse it. At this time, Cassius tells Brutus that many of the most respected Romans, "groaning under this age's yoke" (1.2.63) (the tyranny of Caesar), wish that he "had his eyes" (1.2.64); that is, they perceive better what is occurring.

Then, as Brutus hears the crowd cheering, he says that he fears Caesar has been made king by the people. Cassius replies to him that if this is what he fears, "then must I think you would not have it so" (1.2.84). Brutus replies that he loves honor more than he fears death and would like to know what Cassius has to tell him. Hearing this, Cassius takes advantage of Brutus's great love of honor, saying that "honor is the subject of my story" (1.2.94).

Cassius then launches into a soliloquy in which he describes the "feeble temper," or weak physical condition of Caesar, and he asks Brutus if such a man should become the sole leader of "the majestic world" (1.2.158) when this has not been the intention before (Rome has had triumvirates). To add emphasis, Brutus describes Caesar as a Colossus who stands over the Romans. He then reminds Brutus of his own ancestor of the same name who would not have permitted a sole king to rule:

Oh, you and I have heard our fathers say,

There was a Brutus once that would have brooked

Th' eternal devil to keep his state in Rome

As easily as a king.(1.2.160-164)

Finally, to further convince Brutus, Cassius forges letters, supposedly from different nobles, that indicate that Caesar must be assassinated; these letters are placed where Brutus will surely find them.