Mrs. Olinski almost chooses Hamilton Knapp as the fourth member of her team, even though any sixth grader could tell her what a bad idea that is. As Mr. Singh tells her, "'They [The Souls] worried, Mrs. Olinski, because you were on the verge of choosing another. Such a choice would have been disastrous'" (8.32).
It's not just that Hamilton is mean. Even Mrs. Olinski admits that "bad boys had always held a certain charm for her" (5.19). What's worse is that he's a coward.
All of his bullying acts are a little hidden or secretive or distant in some way. He doesn't call Mrs. Olinski a cripple to her face; he writes it on the board. He doesn't call Julian names; he uses marker to write "I am a ass" on Julian's bag. He tries to slip Ginger drugged dog treats. He gets the audience to chant "arf!"
In other words, Hamilton doesn't take ownership of his meanness. You could even say that he's not confident in himself, and confidence is the other trait that all The Souls learn over the course of the novel. Mean, cowardly, and insecure: Hamilton could never be a Soul.