There are undoubtedly many differences between Brutus and real Roman history, on the one hand, and Brutus and history as it is presented in Shakespeare's play Julius Caesar, on the other. I think we should focus on Shakespeare's Brutus and not try to analyze a Roman who lived over two thousand years ago. In other words, I think the question should not be "Why did Brutus kill Caesar" but why did Shakespeare's character Brutus kill the character Caesar. You can refer to a single soliloquy in Shakespeare's play for all the information about Brutus's motivation you should need. Here Brutus is telling the audience exactly why he has decided to join the conspirators in assassinating Caesar. That soliloquy (in my edition) is in Act 2, Scene 1, lines 10 through 34, beginning with "It must be by his death." This soliloquy contains some words of wisdom which have often been quoted:
But 'tis a common proof
That lowliness is young ambition's ladder,
Whereto the climber-upward turns his face;
But when he once attains the upmost round,
He then unto the ladder turns his back,
Looks in the clouds, scorning the base degrees
By which he did ascend.
Brutus likes Caesar well enough but doesn't really trust him. Unfortunately, it is not in the least uncommon for friends to become enemies. Among other things, Brutus seems to be thinking that he would not be able to remain friends with Caesar if he became a king and a ruthless despot. Maybe Brutus is right. Brutus does not join the other conspirators frivolously but does a great deal of soul-searching. It was not easy for him to stab his friend. He was the last one of all to do so.