In order to answer this question it is necessary to examine particular sections of the text and explore the reasons that the conspirators use for justifying their assassination of Julius Caesar. One of the most interesting sections is the soliloquy of Brutus in Act II scene 1, where, after the seduction scene of Act I scene 2 where Cassius manipulates him to join the cause, Brutus goes over in his own mind the reasons by killing Julius Caesar is a good idea. Whaht is so fascinating about this soliloquy however is the way in which Brutus seems desperate to try and convince himself that it would be a good idea, as this points towards an inner conflict as he struggles to separate his selfish desires from his desire to be noble and to do right. However, note what Brutus states as his main reason for killing Caesar:
He would be crowned.
How that might change his nature, there's the question.
It is the bright day that brings forth the adder,
Adn that craves wary walking. Crown him: that!
And then I grant we put a sting in him
That at his will he may do danger with.
The big fear of Brutus is Caesar's desire to be crowned, and the power that this will give him. Brutus fears that when Caesar is given absolute power through the crown he will receive, this will "change his nature." He draws forth an interesting parallel from nature where he compares the situation with Caesar to an adder, who by night is no danger, but by day comes out and forces people to walk very carefully in case they step on it. Brutus likens giving Caesar his crown to giving the adder his sting, because when Caesar has his "sting," he will "do danger with" it and abuse his power. The most important argument that the conspirators have therefore is the fear of what Caesar might do when he has complete and absolute power. Brutus manages to covince himself with this reasoning that Caesar's death is the most noble and honourable outcome to aim for.