You think it's annoying being analyzed during an interview? Imagine how the general public feels being seated next to a psychiatrist an airplane. (Assuming they're not the portion of the general public that wants to talk about all their problems!) One of the reasons I soured on psychiatry was because I saw during my residency how so many attendings, presumably otherwise normal individuals, had lost a very core part of their basic social skills. Like, don't try to read minds of people in social (or job interview) settings.
A reflex tendency to psychoanalyze others, and to see life in terms of DSM codes and not a whole lot else, is a hallmark hazard of the trade of psychiatry. It isn't going away. If it bothers you now, when you haven't even started, it might bother you more as you have to deal with it on a daily basis, in a hierarchical setting where you have to report to the people who are inappropriately psychoanalyzing you because, well, that's what they've learned to do over the last 50 years, and they long ago lost any idea of how else to interact with others.
Oh, and by the way, if you complain about this, that will be considered "anxiety."