There is one valid reason to not have a pet. If you cannot or will not properly take care of it, you shouldn't have it because that will save the animal quite a bit of suffering. Otherwise, you are better off getting one that you are going to take proper care of, and not sacrifice taking care of that pet so you can work harder to enslave the world.
And that is not limited to dogs or cats. People can and do keep other animals for pets. I have heard of rats and mice as pets, raccoons, hamsters and gerbils, tarantulas, and snakes. The only thing I advise against is jumping into getting a pet and not being able to properly care for it--raccoons can be quite a handful if you don't know what you are getting into.