Maybe you mean to say all relationships with people are senseless (or meaningful) to an equal degree?
Or that the relationship positions, ie. our states, are not unique? That relative to one another we could be anything?
Is this the phenomena referred to as being 'atomised'? Equally disconnected from everything, so that no specific attribute can be accorded greater or lesser weight than any other?
I might not be interpreting what you're trying to say correctly, but I have my own experience of looking at family members etc and just being lost in the realisation that they're strangers, no more or less meaningful to me than any other person, not connected in a sense, because no one can be truly connected. Or of looking at a lover and seeing them entirely free of associations and attachments... seeing them just as any other person.
(Except, on another level we are all connected - this is just one of those circumstances where one has to hold a multitude of apparently conflicting layers of interpretation...)
It's a state of mind. A complete and disorienting (and liberating!) loss of contextualisation. As Luzian said, nothing is truly random, there are just parameters within which we cannot discern the pattern.
Hmmm...perhaps this is a peril of the doctrine of equality?
On a metaphysical level we could hold the argument that all beings, being equivalent, are reducible to the same value and are hence the same, but here in the flesh and blood world we make choices based on preferences and the capacity to discriminate based on discernable attributes. Much is done subconsciously (hence the difficulty in perceiving any pattern). If we couldn't discriminate, that is define the differences between things, we couldn't survive.
And being unable to locate the reason behind a choice or circumstance is not proof of no reason.
hmmm....
edit: and yeah... what Dissident said too.