I'm not sure why Sisyphus is confusing CBT with DSM and medical models. CBT theory is very clear in regarding emotional problems as being learned response patterns rather than medical diseases. One of the marvellous things about working with CBT is the way in which it allows the normalisation of the problems our clients experience.
The idea of an "underlying personality defect" IS, by contrast, a medical-model type understanding, with the pathogen located in the "personality" (whatever that is).
Your supervisor had the right of it in one sense. However, it is worth noting that psychoanalytic treatment of specific phobias is said by analysts (i) to take considerably more than two years; (ii) to not necessarily (or even be likely to) result in any symptom relief. There is no research evidence whatsoever of the effectiveness of psychoanalysis in the treatment of specific phobias.
Personality defect or problem, I wonder?