I think the reason these girls start down the road of thinking that things will be better if they can just get thinner is influenced significantly by the sea of seriously overweight people around them, most of whom are having trouble keeping various areas of their lives under control -- not just their weight. There's a fear of getting onto a slippery slope that others around them are obviously already on. And of course, the onset of severe eating disorders almost always occurs at an age when mentally maturing young women are starting to feel a natural need to exercise control over their own lives, while modern society postpones the feasibility of meaningful control for quite a few more years. Weight is one of the very few areas over which youth in this age range can actually exercise virtually complete control.
What you eat (or don't eat) is the simplest thing for YOU to control. No one can make you eat (truly) if you don't want to...and no one can really stop you from over eating either. So for a young girl seeking order in the chaos she lives in, the simplest solution is to control what goes into her. She is controlling her body, her size. I don't really think their is a rationalization about the size of others...it is all about controlling their bodies/lives to a state of perfection.