Why do the conspirators want Brutus to join them?

When the play opens, it is only Cassius who shows how much he wants Brutus to become a part of the conspiracy he is trying to organize. Without Cassius there might never have been a conspiracy. He knows how to do such things, and Brutus doesn't. Cassius needs Brutus because he knows that he is not popular with either the common people or the patricians. He is not liked because of his character and personality. He is a miser. He is selfish and greedy. He has a violent temper and uses it to intimidate people and to get his way. He is privately thinking that he can be the real power in the conspiracy and use the mild-mannered, scholarly Brutus as a figurehead. But it doesn't work out that way. Once Brutus decides to become involved, he takes command and hardly listens to Cassius' advice.

Cassius thinks they should kill Mark Antony along with Caesar, but Brutus is too noble and too trusting to agree. Then Cassius is horrified when Brutus permits Antony to speak at Caesar's funeral, but Brutus overrules him. Before the Battle at Philippi, Cassius and Brutus have a violent argument in which Cassius threatens to kill Brutus. But Brutus is immune to the kind of scare tactics Cassius uses successfully on other people. After the quarrel ends, Brutus has obviously asserted his dominance, and Cassius just has to go along with him.

The other members of the conspiracy show their respect for Brutus, but they are not instrumental in recruiting him to their cause. It must have been Cassius who recruited them by telling them that Brutus had agreed to lend his name to their cause. They are all glad to have Brutus as their leader because of his distinguished reputation as well as because he is a descendant of the Brutus who drove the Tarquins out of Rome and established the republic. They are all apprehensive about how the masses will react after they assassinate Caesar, because Caesar has made himself so popular with the lower classes. They fear that what could happen is exactly what does happen after Antony delivers his powerful funeral oration. There is mass rioting. Brutus and Cassius have to flee from Rome, along with the conspirators who are still alive.

Brutus is partially persuaded to join the conspiracy because he thinks there are many Romans beseeching him to do so. Actually, the cunning Cassius tricks him. After the two men separate at the end of Act I, Scene 2, Cassius says to himself:

I will this night,
In several hands, in at his windows throw,
As if they came from several citizens,
Writings, all tending to the great opinion
That Rome holds of his name, wherein obscurely
Caesar's ambition shall be glanced at.
And after this let Caesar seat him sure;
For we will shake him, or worse days endure.

Brutus is made to believe that there are many important citizens who want him to lead a conspiracy to assassinate Julius Caesar. Actually, most of them are elated after the fact. Cassius is a "user." He manipulates Brutus into joining his purely theoretical conspiracy by making Brutus think it is much bigger than it is, and then he recruits others into the conspiracy by showing them that Brutus is the leader. If Cassius is not a villain, he comes very close to meriting that title.