How does Harry mature in Harry Potter and the Philosopher's Stone? How is his a coming-of-age story?
In my readings of Harry Potter, I have found that Harry was always more mature for his age because of all of his hardships (living with people who did not like him and treated him poorly) and responsibilities (the chores and tasks his aunt and uncle required him to do). However, I believe that it was Harry's confidence that matured in Harry Potter and the Philosopher's Stone. At the beginning of the story, Harry does his best to minimize his presence, to stay out of the way; of course, that does not always happen, as the various strange incidents that he had experienced can attest. He runs away from his bullying cousin and knows not to ask questions, claiming that as the first rule to a peaceful life with his family (page 21 in the UK paperback edition published in 2014); and when he does speak up, he is either shot down harshly (such as when he suggested staying at home while the Dursleys went to the zoo, pg. 24) or he wishes he had not even said anything (such as the conversation about his dream involving a flying motorbike, pg. 27).
At the very end of the story, when Harry is saying goodbye to Ron and Hermione, Harry shows that he no longer needs to run away from Dudley because he has magic; and even though he cannot use it outside of Hogwarts, the Dursleys did not know that, so he could use it to protect himself (pg. 332).