In general possibility, the opposite of the proposition is not necessary. This broad sense can include propositions that are themselves necessary.
In special possibility, unrestricted necessity is absent on both the affirmative and negative sides. Animality is necessary to a human; laughter is not. They therefore cannot be grouped under special possibility merely because both admit some ordinary-language use of “possible.”
A human can laugh or refrain from laughing. A human's being an animal is not similarly nonessential. The technical word “possible” must be interpreted according to its qualification.