Guy[22M] I'm dating is convinced I[19F] self harm. I don't.

I've been seeing a guy, M, for the last two months, and everything has been going fine. We get along, share lots of common interests and have mutual friends. The only issue so far has been that he often believes he knows more than I do about.. Most things. It's not malicious, but he seems to be working from the assumption that he is generally more knowledgeable than I am. Honestly a majority of the men I've dated have been like that, and I don't really care - he's nice in every other way.
Or I didn't care, until yesterday. When I came to his place, he seemed all serious, in contrast to his usually goofy self - and soon after, he sat me down to talk. And he asked me to see a therapist for self-harm. This would be reasonable - IF I DID! At first it almost seemed like a joke, but when I joked about it, he only said that he cared and wanted to help. I tried to explain that it's my eczema acting up in the cold weather (I live up north) but he didn't seem to believe me. I mean, I said it to his face, and he didn't believe me. After I explained it at length to him (I always get these eczema the same time of year, he just hasn't seen them yet because we haven't dated for that long) he just seemed sad and sort of defeated, and said "okay" - but he obviously didn't believe me. It was pretty weird between us after this, so I actually went home and didn't stay the night - it was just so bizarre.
Also - my arms look a bit bad, but to me it looks nothing like self harm scars! There are spots, not lines, and they certainly don't go deep!
Honestly - I don't know how to feel about his lack of trust, even if it comes from him caring for me. Do I need to bring him for a doctor's appointment? What would you do?
Tl;dr: Guy I'm dating is convinced I self harm, even after I tell him it's my eczema. He doesn't believe me. I don't know how to handle that he doesn't trust me to tell the truth.


Source.