Stories with young protagonists are often set against the backdrop of family life and often fall into the coming-of-age genre. Like here, the young protagonist will go through something big that changes him from a child into and adult, or at least from a child into someone in adult situation, or with adult responsibilities. In "The Scarlet Ibis," Brother begins to comes of age when he decides to teach Doodle to walk.
Brother is a child, but he takes on the responsibilities that should have been taken on by his parents and the doctor. It's great that Brother saw that Doodle was capable of much more than people think, but a little adult support would probably have gone a long way. When Doodle dies, Brother's childhood is effectively lost. He can never be a kid again. In his extreme guilt, he judges himself by the same standards as we might judge an adult.
This is all extremely tragic. Tragedies are powerful not simply because something bad happens to one or more of the characters at the end of the story. Just as important is the story's ability to convey a sense of this didn't have to happen, or, this was completely avoidable. "The Scarlet Ibis" does a great job of this.