What's the more in depth content of these conversations? What does he end up saying? What do you end up saying? Does he know all your reasons for wanting to label the relationship?

If you haven't already, perhaps its preferable inquite about then listen to his reasons for not wanting to label the relationship, rather than having a conversation about it.

If you've already tried that to no avail, and he refuses to open up. Im not sure what to say. In the meantime, if you haven't tried, maybe you can ask him what your relationship status should be called when it's brought up by others.