I went through this with my fiancé and parents last year shortly after I was diagnosed.
As the diabetic, I hated that everyone was constantly asking if I was okay, people would worry at the slightest imperfection in my management, and it made me feel like I was being treated like a child.
Eventually, I had an experience that changed my perspective of things and helped me realize that it was selfish to get angry when my family cared about me.
Help your boyfriend understand that you're not looking to do things for him, but that's exactly why you worry... you're not in control and you probably don't understand the whole story, but want to. He's the one in charge which means he decides when to test, when to inject, and he knows how he feels at any particular moment. Explain that you don't want to help with those things, but you do want to UNDERSTAND them...because you care.
What I wouldn't say, but what is the truth: if he were well-managed and proved it to you, there would be less reason to worry. Since he's not, he owes it to the people who care about him to constantly communicate how he's doing.
This is a matter of empathy and he needs to consider your feelings too. Help him to understand what you see, and why it concerns you. Then ask if he will talk about the things you don't see and explain that you're only trying to understand his perspective of the situation.
I'm not sure how old he is, but this may be difficult for him to understand if he's young. I'm 27 and probably wouldn't have understood where you're coming from if I was 5 years younger....it really is a maturity issue more than anything.