Why is Brutus’ speech at the beginning of Act II in "Julius Caesar" considered sincere?
I don't actually think there's an argument for considering it insincere! Brutus clearly means what he is saying: the problem is that it is an argument which starts - not ends - with a conclusion.
It must be by his death, and, for my part,
I know no personal cause to spurn at him,
But for the general.
Brutus argument is sincere - but unfortunately, flawed. He argues that because Caesar might become dangerous when he is crowned, they should kill him before he is crowned:
And therefore think him as a serpent's egg
Which hatch'd would as his kind grow mischievous,
And kill him in the shell.
It's a very political speech - and it's along the same lines as Brutus' later proclamations that killing Caesar is about killing his spirit, and not shedding his blood. This argument falls apart somewhat when, after killing Caesar, gallons of blood flow freely out onto the floor.