Final answer:
The Llewellyn boys liked J.M. Barrie because of his captivating storytelling and the magical and imaginative nature of his characters and narratives that appealed to their youth and innocence.
Step-by-step explanation:
The Llewellyn boys' fondness for J.M. Barrie, a Scottish author and dramatist best known for creating Peter Pan, likely stemmed from his charming storytelling ability and his whimsical, imaginative nature that could captivate children's minds. Barrie had a way of connecting with children through his narratives, embodying a sense of wonder and magic that appeals to the innocence and curiosity of youth.
Moreover, Barrie's friendships with the sons of Arthur and Sylvia Llewelyn Davies are well-documented, as he became a prominent figure in their lives and their experiences influenced his writing.