Well I went to the shelter looking for a cat. The one I ended up getting really liked me. One might say she chose me. She was a stray and would have been euthanized if we hadn't taken her in. We made up a little story that they found her out back the dumpster behind the Paco Taco and she is tough! Her now-brother, he was from a kitten foster that was not good with cats. Took to my wife instantly. His made up story has to do with sailing and wine it's not as interesting Again, euthanasia issues if we hadn't adopted. I don't know anyone forcing them to breed (cats generally do that themselves unless you get them fixed and while kittens are fun, you want them fixed. TNR works, I help manage... Fuck I don't know how many cat colonies are in the creek anymore. But I have a good cargo bike and good access to cat food. We all kinda take a turn)

But since you asked, people have pets because they like animals and want to be around them. I don't think it gets any more complicated than that.