How do you convince that person to give WoW a shot? Personally, I'd start with the social aspect. Many would-be gamers I know feel worried that they'd be getting into something that's antisocial, that takes them away from "normal" society. To me, WoW is quite the opposite. My family and friends often fail to understand that I'm closer to some of my WoW friends than I am to many of my "real" friends. WoW is an inherently social game, and that's a huge point in its favor.
I might point out the "simple to learn but hard to master" maxim that Blizzard works towards, meaning that the game's learning curve is not too steep, but that there's almost always something you could be doing better. I could talk them through some of the huge amount of content available, and I might just point out that it's nigh impossible to actually "finish" WoW, if I thought the idea wouldn't be too daunting.
Or I might just tell them they can be a pretty elf that turns into a kitty.