In Act 1, Brutus tells Cassius that, though he would not have Caeser as the king, he still loves him. Throughout the play the characters express what seem to be contradictory feelings or act in apparent contradiction to their professed beliefs.
I think you've hit on one of the keys to understanding this play. All the arguments - and all the characters - have two sides. And one of the things that I really admire about this play is that it's very difficult, if not impossible, to make Shakespeare align to one side and not the other.
In exactly the way Brutus hates Caesar as a politician (and would not have him king) but loves him as a man, the play is packed full of contradiction.
So - are the conspirators right to murder Caesar? Caesar does seem to want the crown (if you believe Casca's account of it, where Caesar is "loath to lay his fingers off it"). Caesar is arrogant, referring to himself in the third person. But will he prove a "serpent's egg", and grow up to be a dangerous serpent? Well, who knows? Does he show signs of tyranny? Yes. But proof? No.
In the same way, is Brutus actually an honorable man? Well, he does everything for what he sees as the right reasons ("Not that I loved Caesar less, but that I loved Rome more"), certainly. But he is also a complete tactical disaster, and he gets every decision wrong (see the link to the Q&A post below). And why is he drawn into the conspiracy? Because Cassius appeals to his own arrogance, comparing him (and his own reputation) to Caesar's name and reputation.
Is Brutus a brilliant, committed politican or a woolly-minded liberal? Both - and neither.
(more next post...)
In the same way, Caesar looks at times like an old, frail man, and at other times like a tyrant. Benign old man or terrifying tyranny-in-embryo? Both - and neither.
Is Cassius a sneaking, untrustworthy, lean and hungry villain, or a brilliant tactician who gets all the major decisions of the play correct? Both - and neither.
Is Antony a charismatic, honorable politican, or simply a manipulative man with no scruples who knows how to seize a political moment to his own advantage? Both - and neither.
You see where I'm going with this. "Julius Caesar" is an intensely political play because it is acutely aware that there is no black and white, but only shades of grey. There are two sides to every one of its issues.