There are a variety of reasons why a person may choose to own a robotic pet instead of a living animal of some sort.
For a person who is allergic to animals, the robot is an obvious choice. Persons who live in apartment buildings or have restricted space for other reasons may find it easier to have a mechanized pet that doesn't need to be exercised. Mechanical pets also don't need a litter box, newspapers, or a yard area for bodily wastes. Robotic pets don't need to be fed, groomed, vaccinated, spayed or neutered, and don't become ill with conditions of old age; all of these can become significant expenses when caring for a living pet.
As artificial intelligence systems advance and as robotic components become smaller, the use of mechanized pets will probably increase.