I can relate to the feeling incompetent part. I tend to compare my lack of achievements to others. Not so much to the therapist having a personal life, though. I do tend to hope they're generally happy with their personal life whatever it is, because if they're not that might carry over into their work (me).

This is one thing I was thinking when I read your post. I recently started therapy with a new therapist. I'm an introvert and in the first session he came across as very extroverted. But I also got the vibe that he wasn't judging my disinclination to pursue sociability. I felt that he was interested in who I am and wanted to connect. Therefore, I saw the way he's different from me socially as intriguing. If you can see the differences as just that, differences, and your therapy as using these differences to explore who you are and how you can find ways that make your life more satisfying, it might help you get more of what you want from therapy. I hope this doesn't sound too Pollyannish. It's taking me a lot to get to this point so know it's in a lot of ways counterintuitive.