The main reason why Brutus believes that Caesar must die has to do with the people crowning Caesar as king; he believes that Caesar will have too much power, and may use this power in ways that might not best benefit Rome. For example, Brutus states that, "Crown him?--that;--/And then, I grant, we put a sting in him,/That at his will he may do danger with." (Act II, scene i). In other words, making Caesar king gives him far too much power, and would place him a position that negated the Senate's ability to temper his authority.
It's important to note, though, that Brutus has no personal issue with Caesar. In fact, earlier in this monologue, he says that, "It must be by his death: and for my part,/I know no personal cause to spurn at him,/But for the general. He would be crown'd:/How that might change his nature, there's the question." (Act II, scene i). Brutus sees his intention to murder Caesar as an emotionless, impersonal act that would save Rome from a would-be tyrant.