Chuunibyou means "Middle School Second Year Syndrome" and it's where someone believes or pretends that they are "special" somehow. That they're a hero, or a demon, or have special powers. Usually they do this for attention or in desperation to believe they are something more than average or mundane.
I think you can see why a psychiatrist might diagnose Rin with that. Until he proves he's not kidding by setting fire to things.