Substance is existence simply, accident is dependent existence, relation is co-existence.
Dependency in existence is inequality with respect to it, while co-existence is equality. Therefore relations are distinguished from accidents according to their existence.
While relations are not substances, they suggest substances: a parade, a church, a family and a state are all constituted by relations. Corporations, though constituted by relations, very much suggest persons. Still, this is a metaphor and so what is said relatively is not said substantially.
Objection: there is an inequality in all the things you mentioned; in fact, relations seem to be nothing but a way of standing to a first thing. Where is the co-existence that makes for equality?
Response: to know any of these as unequal requires more information than knowing they are relative, whereas ontological inequality and subordination is of the definition of an accident.