I didn't get the joke, either.
It was a clever joke. Definitely not original work by the DUmmy.
Mental health therapy is based on the concept of "empathy"- the professional understands the emotional state of the patient/client*, and becomes invested in it. Mental health professionals are better at identifying other people's conditions than their own; typically, mental health professionals are psychiatric train wrecks.
So, in the joke, each therapist believes he/she knows how the other feels, but not him/herself.
*In practice, mental health diaqnosis is no more accurate than a TV weatherman's prediction for next weekend. There's an old saying, "Three psychiatrists will give you four different diagnoses".