Clearly, Brutus underestimated Antony. Even though Cassius felt they should kill Antony too, Brutus felt otherwise. Cassius did not want Antony to speak at the memorial for Caesar. Again, Brutus felt that giving Antony permission to speak would be harmless.
Ultimately, Brutus was wrong. Obviously, he had no idea what Antony would say at the funeral. Had he known that Antony would stir the people to a murderous frenzy, Brutus would have reconsidered allowing Antony to speak. He should have listend to Cassius. Cassius was worried that Antony would cause trouble for the conspirators.
Also, the reader is also unprepared for the speech that Antony made. No one expected Antony to be so effective in his speech. Until Caesar's death, Antony had been relatively quiet. After Caesar's death, Antony becomes the Caesar's angel, in much the way Brutus had been at one time.
Finally, Brutus did want to appear as butchers when Cassius insisted they kill Antony as well. In the end, Brutus was wrong about Antony and it costs him his life.
In Act 1, scene 2, Caesar clearly expresses a positive opinion of Antony. He tells him:
Forget not, in your speed, Antonius,
To touch Calpurnia; for our elders say,
The barren, touched in this holy chase,
Shake off their sterile curse.
Caesar patently believes that Antony has some supernatural ability to make his wife, Calpurnia, fertile. Since Antony is participating in a race during the Feast of Lupercal, Caesar assumes that he will be specially blessed. He asks him not to forget to touch Calpurnia because the elders believe that if a runner touches her in the race, her sterility will cease.
It is also evident that Caesar trusts Antony, for he later shares his innermost thoughts with him. He confides in him and says:
Let me have men about me that are fat;
Sleek-headed men and such as sleep o' nights:
Yond Cassius has a lean and hungry look;
He thinks too much: such men are dangerous.
Caesar probably also trusts Antony's judgment because he tells the general that he should not fear Cassius since he is harmless. He tells him that Cassius is "a noble Roman and well given." Antony's advice is, however, erroneous and ironic, for it is Cassius who has already begun plotting Caesar's overthrow. Caesar's reliance on Antony's judgment is more than likely what makes him dismiss all other forebodings. His belief is tragically mistaken, though.
It is quite ironic that Antony does not see Cassius as dangerous when Cassius, conversely, sees him as a threat. Cassius tells the conspirators in Act 2, scene 1:
I think it is not meet,
Mark Antony, so well beloved of Caesar,
Should outlive Caesar: we shall find of him
A shrewd contriver; and, you know, his means,
If he improve them, may well stretch so far
As to annoy us all: which to prevent,
Let Antony and Caesar fall together.
He asks that Antony should be killed with Caesar because he believes Antony cannot be trusted. He believes that Antony is shrewd and manipulative. He suggests that Antony can easily persuade others, and that if he should exercise his ability he might become a thorn in their side. To prevent this, Antony must also die.
Brutus, in contrast, does not share Cassius's sentiment. He believes that Antony is only a part of Caesar and that if the general is dead, Antony will lose his power, for
...he can do no more than Caesar's arm
When Caesar's head is off.
He naively believes that Antony will be useless without his leader. Although Cassius expresses doubt and states that Antony has a deep love for Caesar and is therefore dangerous, Brutus insists that all that Antony can do is to kill himself once Caesar is dead. He emphasizes that Antony is not one for revenge, and that he is more interested in "sports, wildness and much company." The implication is that Antony loves socializing and will, as a consequence, not act against them. Trebonius agrees with Brutus and states that Antony will later laugh about what has happened.
This innocent belief in Antony's goodwill and inability to endanger them is emphasized later when, against Cassius's warning, Brutus gives Antony an opportunity to address the crowd at Caesar's funeral. When Antony speaks to the multitude later, he so incenses them that they turn against the conspirators and seek them out to take revenge.
It is clear that Cassius, because of his inner malice, is suspicious of anyone else and sees risk when it appears to people like Brutus that there is none. It is probably Brutus's inherent goodness that prevents him from seeing anything bad in others. Ultimately, though, it is this lack of judgment that ironically leads to his and the rest of the conspirators' destruction.