Reasons why I don't have a cat*, off the top of my head:

1) do I seem like someone who could take care of a cat?
2) don't want to clean the litterbox
2) take the cat to the vet
4) deal with cat hair all the time
5) make sure it has enough attention so it doesn't take all my stuff apart.

Imagine what kind of cranky old spinster lady I'm going to be without a cat! Perhaps in my old age, I'll be able to handle a roommate, a roommate with a cat, perhaps.

After all, I like other peoples' cats. Just like I like other peoples' kids. And other peoples' dogs. And houses.

* most of these also answer the question, "why don't you have/want kids?"