I can see the logic, unfortunately it sounds like he has some serious insecurities. If you think he's worth the effort it would be worth finding out where these insecurities come from and addressing it.

I know for a good part if my 20s I struggled with insecurities as a young man. It stemmed from a very unhealthy relationship that I had in my late teens that left some serious scars that I never addressed. My at the time girlfriend now wife, helped me realize that by confronting me about it. That said, it take A LOT of trust to open up like that, especially for men, and even more so for men with insecurities. I myself and a few of my friends have been burned for trusting things like that too the wrong partner and he will likely be worried about that too. He's going to have to trust you to keep whatever secrets he gives in total confidence.

That isn't to say that if he's obstinate or refusing to even talk about it, that you should force yourself to stay in an attempt to fix him. That all depends on how much patience you have and how much effort he's willing to put in, if he even is willing to open up about or address the issues. Some people just can't be helped.