The source pairs the appropriate contradictories of necessity with general possibility:
الضرورية ↔ الممكنة العامة
A necessity claim is negated by the appropriate possibility of its contrary.
For example:
“Every human is necessarily a writer” asserts necessity.
“It is possible for some human not to be a writer” expresses the relevant counter-possibility.
Denying that a property is necessary does not mean the property is absent from everyone in actuality.
Keep denial of necessity distinct from denial of actual occurrence.