It is a fact that one object can have many properties and that one property can be shared between many objects.
This fact means that not all objects and all properties can be real (independently of what we mean with “real”), because it would mean that there is a one-to-one correspondence between objects and properties, which obviously contradicts this fact. This fact thus excludes the possibility that all objects and all properties are real.
Instead, this fact means that we have to divide “objects” and “properties” into “real” and “unreal”, independently of what we mean with and which we put in which. Objects and properties simply have to be different in this respect to avoid contradiction.
This fundamental fact is, however, consistently challenged by people called “realists” (like so-called “cladists” and “particle physicists”), which on the contrary claim that both indeed can be real. (Whereof “particle physicists” even claim to have shown empirically that they are, by claiming to have found the so-called “Higgs particle”.) These challenges are thus totally irrational. This matter is not a question of what there is (ie, what is real), but of that not both can be (ie, can’t be real). If objects (eg, particles) “are” (real), then properties simply “aren’t” (real), independently of what we mean with “is” (real). We simply can’t squeeze both into “real” without contradiction.
Acknowledging this fact is called “nominalism”.