In "Fasting and Eating for Health" Dr. Joel Fuhrman has a lot of scientific reasons that explain why fasting is not starving.
It sounds like your boyfriend is concerned for you, which is good. But if he were really concerned, he would become educated, by looking up books on fasting in Barnes and Noble or researching it on the internet. It sounds like no matter what "arguments" you present, he won't believe them coming from you. He needs to understand it's your life, and as long as you haven't exhibited patterns of self destructive behavior in the past, he should trust you to take care of yourself.
Eating disorders and anorexia are a compulsive thing. People won't eat because they feel ugly and fat, and no matter how skinny they become, they still don't think they "deserve" to eat, or because they still "feel" fat, etc. They are emotionally driven compulsive disorders that don't follow any rules of logic and do not bend to rational thought.