Peter Pan is generally considered to be symbolic of not wanting to grow up. He resists becoming an adult and the responsibilities that come with it.
Peter's life in Neverland does not require him to answer to anyone (a child's dream!), go to school, do chores, or think much about his future. All of these responsibilities are normal for children and even adults, so in many ways Peter also symbolizes a desire to escape the real-world and all of its obligations.
In spite of all of this, he does actually perform some responsible actions in the story. He rescues Tiger Lily, Wendy, and the Lost Boys from Captain Hook, after all. It seems that in these scenarios his desires to play the hero or do the right thing might outweigh his desire to avoid responsibility.