It's not actually forbidden, and North Korea does have a tourist industry. However, the official US position is that US citizens are strongly advised not to go to North Korea unless there are very particular circumstances and you have explicite offiical permission from the host country. The US has no embassy there or any official relations at all, so if anything went wrong while you were there, the US would not be able to help you. Relations between the two countries are very poor, and as well as the lack of a US presence in North Korea, there is an added possibility that the NK officials may make difficulties with your application due to this hostility. You can learn more here.

In addition, a lot of people feel that in going to this country as a tourist you are giving financial and moral support to one of the world's most secretive and oppressive regimes; so many people choose not to visit for that reason.