“A human is an animal” is necessary; its opposite, “A human is not an animal,” is certainly not necessary. Thus the affirmation also satisfies the denial of necessity of its opposite. In that broad sense, general possibility can encompass a necessary affirmative claim.
It can also include a contingent predication, such as the possible acquisition of writing ability by a particular person.
Therefore general possibility entails only that the opposite judgment is not necessary. It does not by itself establish that the present judgment actually obtains, fails to obtain, or is equally balanced with its opposite.