It's also worth noting that data collection was entirely done through surveys; so, another explanation could be that therapy simply made people more aware of pre-existing personality deficits, that they were then able to more accurately report.
And further, even if the results are valid, it doesn't invalidate the benefits of therapy; most therapy methods are built around helping the patient. Its possible that therapy improves the subjective quality of the patient's life at the expense of some external qualities (or pretense thereof.)
That's not the case-- they were measuring for subjective quality, and it was subjective quality that declined. I posted the PDF of the paper in my top-level comment, but the Psychological measurements they were looking at in the German cohort were self-esteem, life satisfaction, and depression. The US cohort was measured for self-esteem, chronic stressors, and depression.
no random assignment.
bad temporal proximity of data gathering on personality.
methodological poking about at the badness of controlled vs observational studies. basically study recruitment as a selection effect.