Why do the conspirators want to involve Cicero in the plan? What does Brutus say?

This question refers to act 2, scene 1 of Julius Caesar, in which the conspirators have gathered to discuss their situation. Cassius ventures the idea of involving Cicero in the plan, stating that he thinks he "will stand very strong with us" and that they should "sound" him (see how he seems to feel about the plot).
Cassius and Casca agree, and Metellus Cimber expounds on this, saying that Cicero's "silver hairs will purchase us a good opinion." That is, he feels that because Cicero has a high standing in the city, and because he is an old man, others will believe that the plot has been Cicero's idea all along, and that the young men involved are simply responding to Cicero's leadership. As such, having Cicero seemingly in charge will lend the plot legitimacy, rather than it simply seeming like an uprising of young men who do not know what they are doing.
Brutus rejects this idea, however. He says, "name him not . . . for he will never follow any thing that other men begin." Brutus feels there would be no point in approaching Cicero because he only wants to be involved in things he has thought of himself; he will not want to be the figurehead of an existing movement.