It is impossible to force Karl Barth, the eminent Reformed theologian of the 20th century, into any box, doctrinal or psychological. But I found this comment from Hans Frei the most perceptive I’ve read when it comes to psychoanalyzing the man.
[H]is relations with others, including many long and loyal friendships with other theologians and pastors, seem to have been forged through a sense of common vocation and common moral tasks, rather than through the art of mutual personal cultivation or direct in-depth “encounter.” His intimate relation with his long-time assistant, Charlotte von Kirschbaum, was in its way perhaps the most striking instance of the first type of relationship in his life; his sad misrelation to his wife was his paradigmatic failure in the other kind. . . . To what extent did a sense of shared vocation govern even his intimately personal, sexual life? [Hans W. Frei, Review Article: Eberhard Busch’s Biography of Karl Barth, Historical Magazine of the Protestant Episcopal Church 51:1 (Mar 1982): 111].