Vegans tend to love animals, and that inspires them to follow a vegetarian and eventually vegan diet. (The non-diet part tends to follow afterwards. See it as an on-going process, like learning things in life is.)

Most vegans I know are totally OK with pets. Some own dogs, cats, or horses. Some aren't, and some hate cats for the damage they cause (apparently a big problem in Australia). It isn't common, but some vegans tried to make their cat vegetarian or vegan as well (cats are natural carnivores).

Reading my post back my post it is rather generalising, and vague ("most", "some", lacking sources, and anecdotal). Sorry for that, but hey at least I both state it and admit it.