Not something I thought of before, but obviously true in hindsight. Uniqueness is, by definition, a relation object A has to similar objects B1...Bx. The relation being that A is only one in that group that has a certain set of properties.

So you can he unique among all the people, but you can't be "just unique".

Now, whether the culture of "be unique" and the need to distinguish yourself from other people makes sense, is an entirely different discussion.