Common sense applies to a degree. I was once with my aunt on a motorway. A cat ran under the car and judging by the bump it was hit pretty solidly. No one in their right mind is going to stop on a motorway to deal with a cat.
It's sad but they're animals and on occasion through their own misadventure they run under road vehicles just as foxes, badgers and deer are occasionally wont to do. Depending on what occurs you might not even notice if you're in a larger vehicle.
I drove down a road recently and found a cat that had been hit by a car. Being an animal lover and non squeamish type I stopped and had a look and it was clearly dead and had been long enough for rigour mortis to have set in. I moved the body to the side of the road as I had places to be and it was 5am. When I came home from work it was gone.
On a different tangent my brother once ran over a toddler who without warning got away from his mother and ran right in front of him - nothing he could do and he was gutted. The whole incident was witnessed by a police officer and no action taken but regardless of the scenario you would stop.
That's the difference between hitting a cat and hitting a person.
A dog being larger is also more likely to damage the vehicle.
