Maybe teachers consider Peter fanfiction as something not based on facts or academic knowledge. They are more inclined to believe in materials that are verified and have educational value.
Teachers often have a set of standards for what is reliable information. Fanfiction by nature is fictional and might deviate from the 'truth' as they see it. Also, in an educational context, they focus on materials that can help students learn proper grammar, history, etc. Peter fanfiction may not meet these requirements, so they don't believe it.
One way could be to show how it can be used as a creative writing example. Highlight the unique storytelling techniques in Peter fanfiction.
One popular theme is the exploration of eternal youth. Since Peter Pan doesn't grow up, fanfiction often delves into what that really means. Another theme could be the relationship between belief and magic. If the characters believe in fairies, it often leads to magical things happening. Also, the idea of friendship in Neverland is a big theme. Peter's friendships with the Lost Boys and his relationship with Wendy are often explored more deeply in fanfiction.
Peter Pan himself is very intriguing. His carefree nature and refusal to grow up offer a lot to write about. Wendy is also interesting. She comes from the 'real' world but gets drawn into the magic of Neverland. And Captain Hook, with his villainous ways and his obsession with Peter Pan, makes for a great character to write about in fanfiction.
Peter could be an ordinary person who has been given extraordinary powers for some reason in this fanfiction.
Professor McGonagall could be one of them. She is strict but fair and has a lot of knowledge about transfiguration which could be shared with Harry in a more personal way in this fanfiction.
There might be a young and enthusiastic science teacher. This teacher could be really into modern technology and wants to inspire Sakura to use science to solve problems. He or she might bring in all kinds of cool gadgets and experiments to the classroom, making Sakura see science in a whole new light.
Peter could be a disgruntled noble in the fanfiction. He might be someone who has been overlooked for promotions or honors by the emperor, and this has led to his resentment and desire to kill the emperor.
Peter could be just an ordinary person with an extraordinary love for dogs. He might be a local boy who has always been fascinated by the tower and decides to bring his furry friends along on his adventure.
Perhaps there's been some sort of miscommunication or misunderstanding among Peter and his friends. Maybe a villain has manipulated the situation in such a way that his friends now think Peter has betrayed them, so they've cut off all ties with him. This would create a very lonely and difficult situation for Peter in the fanfiction.
Professor Snape is often very popular in such fanfictions. His complex character in the original series gives a lot of room for creative interpretations in fan works. Writers can explore his relationship with Harry in different ways, like having him be more of a mentor figure in ways that were not fully explored in the books.