People decide to become vegetarian for many different reasons. For some it is a moral issue related to animal rights, for others it is for health reasons, and for others it may be for religious reasons. Many anorexic patients decide to stick to a vegetarian diet, and this is normally interpreted by the therapist as a method of losing weight, or a manifestation of "fat phobia".
Often the type of foods we enjoy are not just a matter of personal choice. Many of us suffer unpleasant effects from certain foods and eventually learn to avoid those foods. For a person with a biliary tract or pancreatic disorder, eating fatty foods like beef or bacon may result in stomach pain, nausea, bloating or vomiting. If this happens on a regular basis, it is very likely this person will learn to avoid meat altogether.
Since there may be a status associated with a vegan lifestyle (in some social circles), this person would find it very easy to become vegetarian. On the other hand, someone who enjoys eating meat and gets no nasty side effects would find it a great sacrifice to become vegetarian.
We tend to gravitate toward pursuits that we will be successful at, and this certainly can be a factor when it comes to food consumption. For myself, it would be very easy for me to join a club that abstained from seafood, since I can't recall ever having a pleasant experience with this food type.
If an anorexic person decides to become a vegetarian, the possibility of fatty food intolerance should be explored through diagnostic testing.