Because Brutus becomes convinced that Caesar, once crowned, would change his nature and begin to abuse power, and that he must be stopped before then. He himself admits, in Act II, scene 1, that he has no personal grievance against Caesar.
In the orchard, Brutus says the abuse of greatness begins when it separates mercy from power, and admits he has never seen Caesar's affections weigh more than reason. Since the complaint cannot be sustained by what Caesar is, he shapes it on what he might become: he imagines him as a serpent's egg that, once hatched, would be harmful, and concludes: "And it must be killed in the shell."
Before this, Cassius works on him (Act I, scene 2): he says that Brutus's name weighs as much as Caesar's and recalls the elder Brutus, who would not tolerate a king in Rome. Then he sends letters that appear to come from citizens, and Brutus reads one in the orchard that calls him to speak and to act.
In the Forum (Act III, scene 2), the public explanation is shorter: he loved Caesar, but loved Rome more, and killed him because he was ambitious. The play never shows Caesar acting as a king. What it shows is the crown refused at the Lupercal, as told by Casca, and Decius's assurance, on the morning of the Ides, that the Senate would give him one that day.