The phrase "[object] is '[person]'" means that the object is a match for someone's taste and personality. If I say "that shirt is very him" it means that shirt fits his personality; it is both the type of thing that I think he would like and the type of shirt that I think he would choose.
"I don't think they're really 'me'" means that the person did not like the thing they were talking about. It seemed to be a mismatch for them (for example, they're a quiet person and the thing is very loud. Or they're very businesslike and the thing is freeflowing).
A "fluid concept" is something that is not well defined. "'You' is a fluid concept right now" is a way of saying that the person is changing personalities and it is unclear exactly what type of person they are and so the object might be a match.