Inuyasha's mother is allowed to take only food for herself, as they refuse to feed the child of a demon. So Izayoi gives much of her food to her child, making sure that he is getting enough. Izayoi is already thin and frail from years of this when she takes ill. Inuyasha realizes this the first time she doesn't have the strength to divide the food into two separate portions.
He needed more food as he got bigger, meaning Izayoi was eating less and less just so he was never hungry. Inuyasha realizes this the first time he feels real hunger, a day after being thrown out into the woods, and after his mother's death. Suddenly, this little seven-year-old boy finds himself being eaten away by the guilt that had she not been feeding him she would have been strong enough to survive the illness.
He resigns himself to starvation as he wanders the woods. Atonement, he thinks, because of the large part he played into his mother's death. He deserves this much for taking his mother's food, be believes. When he's so hungry he can barely process anything around him, he remembers. He remembers finally that it was his mother that did that for him. She did that so he could live. It would be a waste of her sacrifices to let himself die. He has to live—if for his mother, or for himself. He has to.
He catches a fish and eats it raw. Then another, and another. When he can eat no more, he sits back and stares up into the starry night sky. It's so beautiful. The world is beautiful. Life is cruel and cold and harsh, but if he takes a moment to step back and consider that his life means something to someone—means so much to someone that they would sacrifice their health—their life—then he can see his own life for what it's worth. It was worth a lot to someone. It too, can be beautiful.