"The Possibility of Evil" and "Charles" each focuses on a character whose behavior comes as a complete and total shock to the people around them: Miss Adela Strangeworth and Laurie, respectively. Both Miss Strangeworth and Laurie are revealed to be manipulative and deceitful, and both are absolutely tricking the people around them into thinking something that isn't true. Miss Strangeworth has tricked others into believing that she is a benevolent, if eccentric, old lady, while she is really a cruel and heartless purveyor of rumors. Laurie tricks his parents into believing that a naughty peer named Charles is responsible for all kinds of terrible behaviors in his class, when it is really Laurie who is behaving so badly.
Miss Strangeworth, however, gives no real indication of her true nature in her daily life, while Laurie's parents really ought to recognize that they are being manipulated. They pass judgment on "Charles's" parents for Charles's behavior, all the while tolerating the absolute disrespect and even malice of their own son. Thus, "The Possibility of Evil" would seem to suggest that the titular possibility to do evil exists in each of us, no matter how we may appear on the outside: essentially, the idea that appearances can deceive. On the other hand, "Charles" suggests that parents often fail to recognize their own flaws while they are quick to point out the flaws in others' parenting.