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Answering this question in a literal way is inherently risky - after all, in Shakespeare, there is no psychological realism to speak of. People rarely do grand, sweeping gestures and explain them carefully, nor do we get inside knowledge of characters in the same way as we do in modern-style artistic media, such as film, television, or novels. Drama paints with a broad brush, and classical tragedy paints with one of the broadest, in terms of "motivation". That said, Cassius does give hints as to what drives him. He feels a personal offense in the idea of submitting to a "stronger" man, especially since Cassius believes that Caesar is actually weaker - Caesar is epileptic, prone to illness, and not athletically strong. This jealousy and sense of injustice recurs throughout the play and helps explain Cassius' motivations.