They are like them
People like the things that represent them the most. This includes the pets they own. Cat people usually share some personality traits with cats, such as independence, self reliance, cautiousness & introversion.
Random and unexpected
Cats do unexpected things all the time, which makes them very amusing. One of the main reasons so many pictures of funny cats circle the internet is that cats do things unexpectedly that surprise their owners.
Not that outgoing
Cat people are usually not as outgoing as dog people. A person who gets a dog will have to go out often and walk it. Cat owners are usually introverts like cats because they are not obligated to take them out and socialize with other cat owners.
Cats are very funny
Because of their unpredictable behaviour, cats are funnier than dogs. A dog will follow orders and do the usual things they do, but a cat might do something totally unexpected and make people laugh. (See Why Talking Tom Cat got so popular?)
The science of cuteness
So many researches have been made on the effect of cuteness on popularity and most of them pointed out that the more cute a thing is, the more popular it is. Because cats are considered to be very cute creatures, many people love them.
Quiet like their owners
Cat people are usually quieter and calmer than dog people. Because cats share the same personality traits with some people, those people are very comfortable owning a cat. (See What are the personality differences between dog and cat owners?)
Cats have complex personalities
Cats have complex personalities and very expressive faces. This makes them much more interesting to some people.
They see themselves in cats
The more a person has personality traits that are close to cats, the more that person will see himself in the cat’s personality.
They are safer
Because cat owners are usually more cautious, they prefer to own an animal that might not cause much trouble. Yes, cats can cause a few scratches but compare this to what a Rottweiler can do.
People who love both are dog people
If a person has both dogs and cats as pets, he is mostly a dog person and not a cat person.
Why do people like cats so much?
If You Love Cats, This May Be Why | Why Do So Many People Like Cats? Why Do People Like Cats?