I don't know who started the myth that mice like cheese but someone needs to be sued for this lie. According to British scientists doing some incredibly important, cutting edge research, mice actually like things that have a much higher sugar content, such as grains and fruit.
Mice have evolved almost entirely without cheese or anything resembling it. They respond to the smell, texture and taste of food and cheese is something that would not be available to them in their natural environment.
This is almost as troubling as learning that the Brontosaurus didn't exist.