Is my neighbor right to hate my dog?

my neighbor hates my dog because his cat was in our yard and i did not know, my dog was scratching at the door so i let him out to poddy. but i heard my dog bark and ran where he was and he bit my neighbors cat, i grabbed his leash and pulled him back and the cat hid in our shed, i locked my dog in and his cat was fine and was walking normal and let me pick it up and pet it, it even purred, so is my neighbor right to hate my dog, i bopped my dog on the head and put him in the bedroom, but im not sure, is my neighbor right, or overeacting. (keep in mind his cat was fine, just a little freaked)