Her daughter Florence gives Mrs. Deville bull-terrier Baxter as a surprise present. Although she’s afraid of him, she doesn’t want to give him away because she feels lonely. But Baxter has his own ideas – he longs to be dominated, to be challenged – and so he isn’t content with his boring life with the old lady. To get rid of her, he causes an accident. It works, and he’s given to the neighbors, a young couple. He’s happy… for a while. When they get a baby, he again takes action. –IMDb
I saw this as the unlikely elevation to the dog's perception in respect to change from a savage nature to one of acceptance. This's contrasted with the young boy's slow growth from a basic immature nature into a merely acceptable nateure as exhibited in the dogs younger days. so eloquently portrayed in the last scenes of the movie