Peter Pan can be interpreted as a sad story depending on your perspective. The lost boys' search for a home and Wendy's eventual return to the real world might make you feel a bit melancholic.
The sad story of Peter Pan lies in his eternal childhood. He has left behind his real family in some interpretations, and though he has fun adventures in Neverland, he lacks the depth of real human relationships that come with growing up. He constantly faces threats from Captain Hook and other villains in Neverland, and there's a sense of loneliness as he can't fully connect with others who age and change. His story is sad because he's trapped in a state of perpetual youth, unable to truly belong anywhere.
In the story, the Lost Boys are also in a rather sad situation. They are lost in Neverland, without proper families. Although they have fun with Peter Pan, they lack the love and stability that a real family can provide. They are in a state of limbo, neither fully growing up nor having a complete childhood in the normal sense.
Well, one sad part is that Wendy has to grow up and leave Neverland. She has such wonderful adventures there with Peter Pan and the Lost Boys, but in the end, she has to return to the real world and face growing up, which means leaving all that magic behind.
Well, Peter Pan can't really have a true, lasting relationship with Wendy. He is forever a boy who doesn't understand the depth of adult emotions. Wendy, on the other hand, is on the cusp of growing into a woman. Their different states mean that they can't be together in a more permanent way, which is really sad. It's like two people who are so close but are doomed to be separated by the very nature of who they are.
Peter Pan is in love with Wendy. Wendy's arrival in Neverland changes things for Peter. She brings a sense of warmth and home - like feeling. Peter is drawn to her because she has qualities that are lacking in Neverland. She can cook, tell stories, and provide a nurturing presence. Peter's love for Wendy is shown through his eagerness to have her stay in Neverland and be part of his world, although he doesn't fully understand the nature of adult - like love.
Another theme is the idea of loss. As mentioned before, the differences in their natures can lead to a sense of loss. Peter may lose the innocence he once had when he meets Jack and realizes the harshness of the changing seasons. Jack might lose his sense of purpose if he becomes too attached to Peter and the eternal summer of Neverland. This loss of something fundamental to their characters is a key theme in many sad fanfictions about them.
In many Disney Peter Pan fanfictions, Peter Pan does get hurt. Writers may do this to add depth to his character. When he gets hurt, it can lead to different reactions from the other characters in the story, like Wendy taking care of him. It also allows for a different kind of growth in the story. For example, he might become more cautious or learn a valuable lesson about his overconfidence. And it can also create new storylines where the characters have to find a way to heal him, which can be very interesting to read.