This "rule" comes from Dr. Joel Fuhrman M.D. Fasting and Eating for Health, and other fasting literature.
(You'll have to look it up yourself, I'm not going to dig up those books and retype passages for you.)
Although you may have enough fat reserves to fast "forever" you can still run out of nutritional reserves and need time to rebuild those nutritional reserves, more than just a couple of weeks of just eating a few slices of fruit or whatever.
My point however was about the OCD behavior of some of the fasters here. Doing never ending long fasts over and over again, neurotically. The human body can put up with a lot, but at some point that kind of abuse is going to catch up with you. Reasonable fasting is healing, I'm sure, but that's not what I'm referring to.