Gee, that's really hard to answer because it depends on so many things. Why is the person resistant? Does that person think that WDW won't have anything that he or she is interested in doing? Does she or he believe it's just for kids or for families or whatever?
In general, I suggest letting that person know that there's something for everyone at WDW. For instance, when DH and I first were negotating vacations he wasn't quite sure what to make of the whole Disney thing. He never said it, but I think he was worried that I suffered from Mickey Madness. I do, but I wouldn't call it suffer. (I'm proud to experience Mickey Madness!)
But I also think DH was worried that a trip to WDW would end up being a trip all about me, me, me, 24/7 and he wouldn't find anything he was interested in. Worse, that the trip would be all about the Mouse and the Mouse alone. So when we were planning our first trip together, I promised him that the trip would interest him, too. I made sure to include things that reflected his interests: a visit to Epcot's Norway, wine-tasting in the different countries, a day at the water park, a map of the resort's running trails, etc. For the attractions, I made sure he had lots of background information on Imagineering and knew some of the trivia. And I planned plenty of couple's time, so he would know the focus was on our trip TOGETHER, not on my trip with him as a tagalong. This meant I didn't get to do a lot of things I would normally do, and that my usual commando-touring style turned into a much more leisurely tour of the parks. But DH ended up loving WDW more than he thought--even if not as much as I do--and now when we visit, he's usually the first one out the door in the morning.
So, although I don't know the particulars of your situation, I would say a good start would be to have a conversation about what you and the other person want from a trip or vacation. Then you can talk about how WDW might appeal to both of you.