Brutus has listened to Cassius and has been given evidence that Caesar is an ambitious man who craves power--he denies the crown, but it is made obvious to the crowd and to Brutus that Caesar does crave the position and the power. It will only be a matter of time before Caesar is Rome's Emperor when Rome had always been ruled by a group of men in order to prevent power from overwhelming and tempting a single man into dictatorship.
Brutus is at war with himself since he has no ill will toward Caesar. However, with the best interests of Rome at heart, Brutus agrees that Caesar is dangerous with the following quote: “And therefore think him as a serpent’s egg, / Which, hatched, would, as his kind, grow mischievous, / And kill him in the shell.” Therefore, he deserves to die, and he agrees to join the conspiracy to rid Rome of its poisonous serpent.
Some critics might add that Brutus is naive and too easily swayed by Cassius, who puts the ideas in his head to begin with in Act 1 Scene 2. Cassius tells Brutus, who suggests he doesn't quite know what to think about Caesar, "Since you know you cannot see yourself / So well as by reflection, I, you glass, / Will modestly discover to yourself / that of yourself which you yet know not of" (67-70). If Brutus doesn't know what to think, well then, Cassius will help him out, and this eventually leads to Brutus's monologue in the garden when he decides Caesar is a danger to Rome and should therefore die.