Always remember cat body language, people who are very scared of cats or dislike them tend to turn their heads or bodies and not to look at them, cats take this as: hello I'm being polite, come over to me if you like, where as people who see a cat and stare directly at it making eye to eye contact, this says to a cat: I am rude and don't have much social grace.
Look at the way cats behave towards each other, the only time they stare at each other or maintain eye contact for more than an instant is when they are about to fight, and they tend to close their eyes at other cats to show they are amenable.
So if you think a cats being mean by bothering a person who seriously dislikes cats, it's not and if you want to approach an unfamilliar cat and get friendly, don't whatever you do maintain extended eye contact, the cat will most likely just run off considering you a threat as you approach, but of course it depends a lot on individual animals, it's a good rule of thumb though.
About 8 years ago when I was doing part time summer postal work I found I could approach most cats by obeying their ettiquette, some I could even pet even though they'd never met me before. I was a regular Dr Dolittle

Dogs on the other hand are simple,they will either bark and growl or be all over strangers depending on their masters reactions, as a defauilt if their master is not present they generally growl and act aggressively, although not always, depends on the breed alot.