I never addressed problems about making/maintaining human connections in therapy much, but have an opinion on the topic. I think many people who try this get stuck in it... instead of focusing on their everyday life and relationships, they get entranced in their feelings for the therapist and the T relationship, that becomes a center of attention, while still no change in "real" relations. And many therapists encourage this even when it becomes clear that the client has expectations and wishes that go beyond the scope of therapy. The relationship with a therapist is very unnatural and limited by default. It may be good to increase awareness to patterns and learn to become more comfortable with sharing private material, but if the therapy fails to encourage the client to focus and apply the lessons to everyday human connections, it will likely create a sort of parallel universe that might even distract from real life improvement.

I do believe that therapy can be useful to work on relationship difficulties for some people, but it needs to be translated and integrated into the connections that are meant to be improved, instead of keeping it isolated in the therapy room, even just mentally.

I do personally believe that the best way to work on social isolation is to make more connections in everyday life (so joining a club may not be a bad idea), and more than just with one single person. I think it is perfectly normal if someone is very lonely, does not have friends etc, but craves contact regardless, if they find one decent, compassionate person, they will likely focus too much attention and expect too much from that single individual. Then every perceived disappointment is amplified. Therapy can be good to discuss and reveal blocks to social life, but ultimately the change needs to occur outside of therapy, and if a T fails to recognize and encourage that, it's probably not a very good T.

If you are satisfied with this T in general, I would not leave over this but would rather push him a bit to talk about it in detail.