The main problem in the story is that the main character, Peter Pan, does not want to grow up.
To grow up means to assume adult responsibility, and Peter Pan desires to be a child forever. In Never Land, this is possible, and Peter convinces Wendy Darling and her brothers to come to Never Land so that she can be a "mother" to him and the Lost Boys, and read them stories and take care of them. Although Peter does defend the Lost Boys, his priorities are adventure and having fun, and he refuses to take on a "father" role because of the serious and often mundane responsibilites that would entail.
In contrast to Peter, Wendy has a well-developed sense of responsibility. When she finally realizes that she cannot stay in Never Land because her parents back home need her, she faces a quandary which she solves by inviting Peter and the Lost Boys to come live with her and the Darlings. Peter, however, knows that if he does, he will be forced to grow up, so while the Lost Boys remain with Wendy and the Darlings, he returns to Never Land, where he lives forever young, but alone.