Upon hearing of Caesar's death, Antony requests to be allowed to speak to the conspirators so he might learn the reasons for the murder. Antony assures the conspirators that he does not doubt their wisdom and offers to shake hands with them, making it seem as if he is sympathetic toward their motivations for killing Caesar. More importantly, Antony asks for permission to speak at Caesar's funeral, and this request is the root of the disagreement between Brutus and Cassius.
As Brutus is a good-hearted and trusting man, he agrees to let Antony speak, saying, "You shall not in your funeral speech blame us,/ But speak all good you can devise of Caesar,/ And say you do 't by our permission." Thus, Brutus decides to allow Antony to speak at the funeral after Brutus has finished speaking.
Cassius, though, is wary of Antony's intentions and says, in an aside to Brutus, "I know not what may fall. I like it not." Brutus, however, dismisses Cassius's worry.
Similar disagreements between Brutus and Cassius occur at other points in the play. In Act 2, scene 1, the two disagree over whether or not to kill Marc Antony at the same time they murder Caesar. Brutus insists that Antony is "but a limb of Caesar," and will have no power once Caesar is dead. Cassius, on the other hand, does not trust Antony and thinks that he needs to be killed, also. (Similarly, Brutus and Cassius disagree with regard to battle plans in Act 5. Brutus believes that their army should advance to meet Antony's army at Philipi, while Cassius insists that it will be better for their army to rest and let Antony's army tire themselves out by journeying to Cassius's and Brutus's army.)
In the case of each of the above-mentioned disagreements between Brutus and Cassius, Brutus ultimately gets his way. However, though Brutus's plans seem well-thought-out, they prove, once executed, to have been major errors in judgment.