They apparently can eat just fine. It's their attitudes about food and body image that are f***ed up.
I'm incredibly hard-pressed to consider these behaviors a "disease." If it was a genuine disease, it'd be showing up all over the world: America, Europe, Russia, Asia and even Africa. But as it stands, it's only in nations in which everything is so okay that people have to make crap up to be miserable about.
Mental illness is a disease. Not viral or bacterial, but a disease none the less.
Calling a problem a disease is often times a cop out, and a way to excuse irresponsible behavior. Calling shoplifting a disease is one good example. But don't be tempted lump in eating disorders. Anorexia and bulimia are forms of mental illness.
As far as why we only see this illness in the western world - there's not a short answer to that. There are other examples of aberrant behavior and emotional states that are regional. In Japan there is a phobia that is common in men that their penis will retract into their body while they sleep. Some men actually have injured themselves by attempting to secure their members outside their body with a rock and a string. This problem is unheard of in the United States. Anorexia is just as uncommon outside the US. That doesn't mean it's not real.
While I realize that there are people who die of this and I don't want to make light of it, there was a commedian I heard once who said the following...
"Only in America could we have something like anorexia or bulemia... Those aren't "eating disorders." Now, Jeffery Dahmer... That's an eating disorder!"