There were parts of this story that I really liked. I loved Henry's attitude, it struck me as being very similar to a stereotypical cat's attitude. He wants to be independent and a little aloof but clearly craves The Man's attention and approval. He can do most of the same tricks as the dog, Buttons, but only because he wants to and never on command. Cat-like indeed.
I think the story could be interpreted as a story intending to help a child with a new addition to the family.
But for some reason the fact that he was walking on his hind legs really bothered me in this story. It's a familiar trope for this series, we've seen it in pretty much ever book. I think it's because this time much of the book was about being able to do tight rope walking like activities with the companion focus on balance. Cats are much more steady on four legs than two and besides, it would have been much more cute to see Henry carry the stick in his mouth rather than his paws. Ah well, still a very fun story. And the gruff The Man was perfect, as usual. (Though I did have a heard time believing he'd call the dog "cute as a button").