Equality is not a relationship. The word implies that two things have the same relationship to a third thing, but they may have no necessary relationship with each other. If two people are equal before a common entity, and that is the extent of their commonality, they in fact have no relationship.
Since equality has become the touchstone of justice and the goal of human relationships, the search for equality easily and often transmutes into alienation. The love of equality produces loneliness.
The only human relationship truly marked by equality is friendship. But this is something different from what the modern sensibility, at hearing the word “friendship”, thinks of: a state which is just a mutual abrogation of any authority or accountability.
Order lies at a level deeper than what the ancients called the “accidents”. Likewise, relationship lies at a level deeper than the accidents.
Much of what we call “personality” is simply the accidental phenomena. A personality cannot be in relation.