Mrs. Darling offers Peter the chance to be adopted into the Darling family after he and her children return from their adventure in Neverland. This, however, means that he will grow up into a adulthood.
Peter turns her down. He is willing to give up the comforts and security of family life because he loves being a boy and wants to stay one forever. If he joins the Darling family, he loses that. That means that his imagination will gradually fade, and as happens to Wendy, he will gradually lose the ability to fly. Adulthood means losing the sense of joy and wonder that childhood brings. It means taking on responsibilities, taking care of others, and eventually experiencing old age and death.
Peter's eternal boyhood comes at a price: he will never experience the gifts that maturity offer or gain the wisdom that comes from assuming responsibilities. He will endlessly need to find a new set of children to take on adventures with him. Nevertheless, he is the symbol of the eternal child: innocent, joyful, and carefree.
It is easy to see why people who refuse to grow up are said to suffer from Peter Pan syndrome. It can be a temptation to want to stay in a state of eternal youth living in an endless party, but it is also sad, too, which is a feeling that the story captures.