Anorexia (and sometimes Bulimia) is often a matter of not just control, but the delusion that the person in question is overweight, ugly, etc, etc, and that is the starting point for a body disphoria and self hatred.
Depression sometimes goes hand in hand with these eating disorders and depression is something I've heard best described as "the absence of hope".
If you already hate yourself, hate your body, and you feel completely derived of hope, then what do you have to live for?
It's common for people to think of suicide as the easy way out, the coward's way out, or the selfish way out. If someone truly believes that he/she are not worth loving, not worth being with, not worth living in general, he/she can come to the conclusion that the right thing to do, by them and Everyone around them, is to stop participating in life completely.
Or, at least that's how I understand it.