The main conflict in Peter Pan is that many characters in the story, primarily Peter, do not want to grow up. With growing up comes responsibilities and obligations. Although children also have their own obligations, like school (which Peter also does not cater to), adults clearly have more accountability and responsibility, and Peter Pan resists this.
Despite the fact that Peter does not wish to grow up, he is the leader of the Lost Boys and he does take on the rescues of several of his friends. He is not entirely without leadership traits or responsibility to his friends.
In the real world we even refer to people who seem to be perpetually childlike as having a Peter Pan Complex, meaning that they also resist most things that come with adulthood and fully embrace the lifestyle, hobbies, and nostalgia of their childhood.
The main conflict in Peter Pan is the conflict between growing up and keeping your innocence. If we become so cynical that we no longer believe in the innocence of youth, we will forget how to fly.
as i see it, Peter is terrified of feelings. of any kind, and part of the transformation from boy to man is emotions; strong once such as pain, love, jealousy, and he, being a smart boy, is realizing that, but doesn't have the tools to deal with it so he's practically fighting himself. (Hook represents every bad feeling there is and peter See's him as an alter ago for all the adults in the world.) peter is proud, and See's feelings not only as the enemy, but as a great weakness. and if he's weak, then what is he worth? how could he survive?