Why does Jess choose the puppy as Leslie's Christmas gift?

Because Leslie says to him that he is lucky to have asister. He replies, "Yeah, well I havefour of them, and I'd trade them all for a good dog." Leslie them says, "I would love to have a dog." Unless you are referring to the book, in which I am less familiar with. I think Leslie thinks this way, because her parents are often busy writing books.