if a dog runs out, nasty as it it, its not going to do much damage to a car
same with cat/other animal
once you get to an animal big enough to roll up and hit the windscreen, i.e. a dear-notice the nice big antelers on its head ready to come through your windscreen....
then you can stop because a life is at danger-yours
if you stop for a rat you are putting your life and the life of thepeople on the roadwith you - suddenly stoping/skidding ect ect your liable for damage
saying to the policeman "but i stopped for felix" wont help you out much....