This makes me sad to think that any cat would be distressed at being petted. Most of my cats were pretty friendly so I never had to chase them down to be petted. But cats aren't as domesticated as dogs and that could explain why some cats hate being touched by people. It also might be because of where the cats are being petted. I've only known one cat that really loved being scratched on the stomach while the others would turn into a ninja and slice up my hands. Also, most people tend to pet their cats the way they pet their dogs and that doesn't work for most cats. I noticed that most cats really love gentle petting and soft scratches. If they want a harder scratch they will simply lean harder on your hand instead of you deciding for them and scratching harder. With dogs, you can get away with petting a little harder for smaller breed and almost roll the bigger dogs back and forth like bread dough. As a rule of thumb, I never chase down a cat but allow the cat to come to me if it wants to be petted and I let them decide how hard I pet or scratch them.