Exclusive, but not dating? What does that even mean?

Breanne
A few weeks ago, my s/o and I had a brief talk about what we are doing. He said he feels we are exclusive so I agreed and took it as we are dating. A couple days ago, I asked him if we were dating via text and he said negative, and reminded me he tried bringing up this subject a few weeks ago. Well we talked about this again in person and he said that he was been exclusive with me, hasn't been fooling around with other girls since we started to do so months ago, but he does not want a relationship. 
The kicker: we went on a 4 day vacation alone in January, we go on dates (take turns paying for each other, he has bought me an NHL shirt, he stays the night at least once a week and has even began leaving a couple hygiene products here. Furthermore, he's met my family and I joined his for Easter lunch.. so I don't know what this guy is trying to say. 
I think we are in a realationship, but I don't know why he's scared to use those words. Side note: My anxiety makes me feel I'm just a place holder until a girl he has (probably does) like wants to date him. I ask him about her and he agrees he is attracted to her, but says he doesn't think it's work with her and several of his male friends told him they think he and I are good for each other because of how loyal I've been since I've known him and he has ran around.