Cassius states that Caesar is no greater than he or Brutus (by birth), and is indeed a lesser man physically. So he feels it is wrong that he should be the one and only power in Rome, especially a Rome that was a Republic -- and therefore all Roman men share political equality (ideally). He also implies later that Caesar doesn't really like him and that upsets him: he isn't part of Caesar's inner circle.
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Cassius didn't like Caesar because he was jealous of Caesar. He believed that Caesar didn't deserve to be king, and the thought of Caesar with the crown got him very angry, he strongly disliked the idea of Caesar with the crown.
Cassius informs the other conspirators that one reason he believes Caesar should not rule Rome is because of an instance when he demonstrated great weakness. He is referring to the time when caesar challenged him to swim in across the storming Tiber. However Caesar was unsuccessful in swimming through the raging waters and even needed help from Cassius getting through them.
If your question deals with the play, I don't know; but if your question deals with the reality of Marc Antony and Caesar, it is easier to answer as Antony and Caesar's relationship is well documented. Antony was a distant cousin or nephew of Caesar. He came up politically and militarily due to Caesar's patronage. Because of this, Antony was a strong supporter of Caesar's. They had their differences, but always reconciled.
It is unknown what part of Caesar's body was stabbed by Brutus. It is a certainty that Brutus, as one of the chief conspirators took part of Caesar's assassination.
It made the government too powerful
The conditions which surround us best justify our co-operation; we meet in the midst of a nation brought to the verge of moral, political, and material ruin.
Tiberius Claudius Cogidubnus (Usually known mononymously as Cogidubnus)