What you speak of maybe circular but it hardly qualifies as logic. Circular reasoning is a fallacy.
The therapist asked a very reasonable question which you acknowledge unmasked a belief that has no basis in reality. What you and your therapist are dealing with is the too often present cognitive distortion. See here: http://psychcentral.com/lib/2009/15-...e-distortions/
While challenging the distortions may be difficult, it should not be so unmanageable when as here the premise is so patently false.
I assume we all want to get better. Challenging every negative we believe about ourselves is a good start. As Descartes said, “If you would be a real seeker after truth, it is necessary that at least once in your life you doubt, as far as possible, all things.