In ordinary thought and language there are obviously particulars and it is assumed they usually consist of parts. Ordinary language also supports "generalized, reified properties" (I'd say they feel like universals) and abstract entities: "Red is my favorite color", "Einstein discovered E = m c²", ...
But in extra-philosophical discourse claims like "There is no X" happen, even when it is common and not bizarre (in the languages of the world) to speak of X like it is something that exists; or when most people would state that X exists.
The easier examples are odd particulars (?) like holes or semi-legendary figures (Laozi). Then, composed entities are sometimes denied to exist, in favor of only their parts existing ("there's no such thing as society"). Certain properties or groups and abstract objects are also regularly denied to exist (e.g. "biological sex does not exist").
The most basic way of looking at the problem is distinguishing (A) "What is?" and (B) "How is it?". The same state of affairs can be described more in the manner of answering (A) or (B) -- and from this preference it depends on how easy it is to deny existence without coming across as self-contradictory.
E. g. say, historians conclusively (according to their standards) discover that there was indeed a Chinese man named Laozi in the 4th century BC, but he did not write the Tao Te Ching and was an unimportant peasant. Did Laozi not exist (preference A), or did he exist and people just have very wrong beliefs about him (preference B)?
If composed things are denied to exist, but other composed things are not denied existence, what might be the standard applied here? E. g. Margaret Thatcher believed families exist, but not society.
If properties or groups are denied to exist, but not tout court, what might it mean? E.g. someone who denies "biological sex" but not "humanity".
Now I ask if there is any common ground in those assertions of non-existence? What does it mean extra-philosophically for something to not exist (aside from the most uncontroversial and widely accepted non-existences like witches). Is there some common thread behind such claims, are they made somewhat coherently and in good faith, or are they just either some incoherent confusions or rhetorical devices to exert power?