When Mrs. Darling offers to adopt him, he declines because she would send him to school and then to an office. Even if he took her to Neverland, she would try to protect him, impose rules on him and teach him right from wrong, keeping him from having the wild, childish adventures he lives for.
Peter Pan wanted to be adopted as he had the realization of the responsibilities of adulthood, and it scares him a lot.
Peter is violent, callous, and heartless. He is not quite a child, because he has lived so long, and he is not an adult, because he does not have to love another or fear death. But Mrs. Darling’s kiss is still for him and him only, for Peter is everything we love about childhood that is not true. His other qualities are only side-effects.
"When Mrs. Darling sees them, she resolves to adopt them right away. She wants to adopt Peter too, but he refuses. He will live in Neverland with Tinker Bell. He asks Wendy to come with him, and she almost says yes, but Mrs. Darling reminds Wendy that she needs a mother too. Peter promises to return for Wendy every year so that she can help him with his spring cleaning."