First, dieting is never a good idea for your child under twelve or thirteen, unless directly supervised by a physician. Even a day or so of eating little to nothing is dangerous for pre- adolescent children. While your child's food is severely restricted, he does not grow. Even worse, he may never make up for the time he was not growing. This is very serious. A young child should never diet unless medically supervised. It is as simple as that.
For a teenager, watching his weight is usually not a problem, although checking with a physician is a good idea. Your adolescent's eating little to nothing for a day or two once in a while usually does not hurt anything; but be sure the dieting is not extreme. Further, be sure it does not go on for more than a couple days at a time and does not happen more than once in a while. If your child has a weight problem, arranging for him to talk with his physician is the place to start.
This sign is part of an eating disorder called anorexia and has little to do with dieting or normal weight control. Your child exhibiting this sign is starving himself. The first thing you notice is his losing weight. Next, you notice his getting thin and eating little to nothing. He might tell you he is watching his weight, is not hungry, or does not feel well. Whatever his reason is, he is not eating enough.
Even though your child is already thin, he thinks he is fat or at least thinks he is overweight. How he looks to you does not fit with his perception of himself. His self-perception is distorted or does not fit with how he really is. He has lost his ability to judge himself and feels fat no matter what the truth is.
If you see this sign in your child, his need for specialized help is urgent. You nor your child can handle the problem without help. Your child can die from the behavior. It does have to do with depression and low self-esteem; but it is much more complicated. Specialized care is always necessary.