Hi,
An interesting dilemna. Here's my thoughts, FWIW, given I know very little besides the few paragraphs in your post.
I would tend to want to go "back to basics", in the sense of the very beginning of therapy. Since therapy can't proceed unless someone wants it, and wants to change, and has realistic goals, I would wonder what this person's goals are. Why does he want CBT; what would he like to see different if it helps? Perhaps you are thinking the goal needs to be to change what you view as illogical thinking. However, this client may not share that goal. Can the two of you find a realistic goal that you can both agree on? I think some people are just not good candidates for therapy, as they have unrealistic goals, such as "I want to be happier in a messed up world, but I don't want to change my belief system" Then again, if that is the problem, perhaps the initial work needs to be on identifying his main beliefs, and having him look at the advantages and disadvantages of holding the beliefs.

Not sure it this is of help, but these are my initial thoughts.

Neil Levitsky