How does Cassius persuade Brutus into helping kill Caesar?

Cassius's argument is that Caesar has made himself into a god and is therefore a danger to the Roman state and the Roman tradition of equality among patricians (the Roman upper class). He recalls those instances of having rescued Caesar from drowning and of Caesar nearly dying with fever so that he cried out "as a sick girl." But now, Cassius says, Caesar has the effrontery to make himself the master of all Rome and to "bestride the world like a Colossus."
Brutus is a member of a long-standing patrician family and thus, in Cassius's view, should resent Caesar's pretensions to power. Cassius's appeal to Brutus is both personal and political. Not only is Caesar unfit to be the man in charge, but his dictatorial stance will lead to the destruction of the Republic, the system by which Rome has been governed since the dissolution of the Kingdom.
By extension, in my view, Shakespeare is at least implicitly analogizing the threat of Caesar to Roman freedoms with those threats to English liberty which existed in the past and were dealt with. Since England, like Rome 1500 years earlier, had had its own internal disorders before the stability of Queen Elizabeth's reign, English audiences of Shakespeare's time could easily relate to the arguments used by Cassius to persuade Brutus to act against what was seen as the tyrannical rule of Caesar.