Brutus thinks that once Caesar is given power, he will become corrupt. To prevent him from bringing harm to Rome, Brutus is wrestling with the idea that he should kill him.
Brutus actually has no specific evidence to think that Caesar will become a bad ruler. He says,
"...for my part I know no personal cause to spurn at him" (II,i,11-12),
yet speaking generally, he is afraid that power
"...might change his nature, there's the question" (II,i,13).
Brutus believes that if Caesar is crowned, that will put in his hands the capability
"That at his will he may do danger with...Th' abuse of greatness is when it disjoins remorse from power...And to speak truth of Caesar, I have not known when his affections swayed more than his reason" (II,i,16-21).
Because of Caesar's personality, and in particular his tendency to be completely unemotional while relying solely on reason, Brutus feels that there is a great possiblity that he will let power go to his head and do damage to Rome. Remembering situations where those who have climbed the ladder of ambition have turned their backs on their more noble inclinations once they have achieved their lofty positions, Brutus reflects,
"So Caesar may. Then, lest he may, prevent" (II,i,27-28).
To protect Rome from what Caesar might do once he is in power, Brutus resolves to kill him, like "a serpent's egg" (II,i,32) while still "in the shell" (II,i,34).