What does that mean if a guy says he's sensitive?

Anonymous
How am I supposed to treat a guy who is sensitive? Anything I need to be aware of?

This guy I am seeing said I hurt his feeling by answering him no without explaining the reason when he asked me if I would be seeing him on a certain day. He went on and said how if I did not want to do that I could have just told him straight out because he's a big boy. I was busy doing something else at that moment but talked with him like 15 minutes later and told him what I would have to do so would not be free. I thought that's done, but apparently that hurt feeling stayed with him until hours later. He left without even saying goodbye (he later on said I was "busy" so did not want to disturb me). And he was talking in a low sad tone hours later telling me it's just because he's a sensitive person and I have hurt his feeling today.

I mean, I get it if I never told him why I won't be seeing him, but I told him later already, so what's the big deal? I didn't want to, and I didn't apologize for it because I don't think it's such a big deal that I have to apologize for. He is quite manly physically and behavior-wise, and he repeatedly says that he's "a real man". It just doesn't quite line up that a real man would get upset for that little thing. Is he really sensitive or is he trying to manipulate me into doing what he wants?
What does that mean if a guy says he's sensitive?
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