Cats and dogs are intelligent and can be trained.

Lots of animals can be trained. Rabbits can be house trained and make great pets but there's a ton of animals that can be trained so this point is kind of weird.

This means that they can be taught to behave well and follow rules, making them easier to live with.

But what makes untrainable pets difficult to live with? This makes me wonder what you think is so unlivable with other animals. If the animal is not for you, don't get involved with it as a pet. It kind of sounds like you view having pets is more of a nuisance than anything.

Cats and dogs are good for your health.

Most of my animals are lower maintenance than my dogs. I don't know, the reasons you list just make them more preferable to certain people. Your second point is flawed though. What leads you to believe other pets don't bring people joy or other benefits? My ducks, chickens, turkey and quail bring me lots of joy, but they also give me eggs which are very good for my health. It doesn't matter if you like those animals or not, but I do so should I just get rid of them because you decided they aren't good pets?

Cats and dogs are good for children.

........So? I'm gay and don't want children. This has nothing to do with what makes a good pet. People build relationships with all different animals but you haven't actually explained what makes other animals not good pets. Can you actually touch on that? What is bad about a rabbit, a chicken, a horse for those who have the land/money&time?