When a person says “I want to be loved for who I am” or “I want someone to love me for me”, what this usually means is that the person has certain specific aspects about them that were never valued, appreciated or wanted. Potentially they have been rejected for those things in the past. Or potentially, those things have never been adequately recognized. On top of this, they may have been valued, appreciated and wanted for something that they don’t want to be valued, appreciated and wanted for.