That's not actually what the article says. It's saying the that sense of identity was mostly experienced as a set of relationships and roles and that an identity distinct from any role or relationship became more common place after mirrors and the clear self picture that provided to people.

It's also not "plainly false" ... most people identify themselves by their roles and relationships. If you ask people to describe themselves they will universally use role and relationship descriptors: computer programmer, cop, Catholic, mother, grandfather, ... It is common for people who retire to have difficulty with the loss of identity that their job and role their occupation provided.