“Thick skin” is a provocative notion about which all new therapists should consider, then reject.
In my work and with those younger therapists with whom I’ve taught and consulted, I do the opposite. I try to help them become even more vulnerable to all the vagaries that can, and do, arise in therapy.
Without emotional vulnerability to our patients, we have no way to enter their worlds, and, therefore, can be of no lasting help.
You may be more broadly asking how those of us who do this work keep ourselves going in the face of the natural stresses of this work. How to care for ourselves is a more pertinent question for those of us who work with people who experience extreme mental states: Borderline personality disorders, narcissistic personality disorders, and the psychoses.
Significantly, we all need our therapists as well as consultants, along with routines that help us unwind and engage in pursuits unrelated to our work. Strong friendships and a loving family are essential.