I've never bought into the whole detox idea. I don't see any logical reason why your body would hold onto toxins until you stop consuming them, and then suddenly release them.
I could see how someone could go through meat withdrawal, though. Most meat is very high in fat, and it's a different kind of fat than you'd find in plants. Consuming fatty foods is a pleasurable experience for most people, and any short-lived pleasure can become an addiction.
My boyfriend is a big meat-eater; until recently, he hated vegetables and generally avoided them. (He's coming around, though; he devoured my tofu and vegetable stew the other night!) Whenever he finishes a meal, he goes half-comatose as his body diverts energy toward digesting those complex fatty acids. I know the sleepy feeling well, although I never got it as bad as he did; for me, a complete meal has always been at least half plants. Now that I avoid animal products almost entirely, I don't get that feeling after eating at all. But I remember that it had a certain coziness to it; there was a very satisfying sense of relaxation layered under the weary, stuffed feeling. It's a little like smoking pot, actually. Not everyone likes the feeling, and not everyone who does like it is equally attached to it. But people who are really hooked on that cycle might go through a sort of withdrawal when they give it up.