I don't feel bad about killing animals, but I'm squeamish about it. I'm fine to catch a mouse in a glue trap where I can't see it, but I would not want to like smash him with a club or something. I like the idea of the challenge and marksmanship of hunting, but would never hunt because I have no interest in getting up close and personal with a dead animal.
Driving, I feel no guilt about hitting anything. I've trained myself to feel that way, as I never want to end up in a ditch or oncoming traffic to avoid a cat or dog or a squirrel. Don't get me wrong, if I'm driving along and see a dog up ahead in the street and can slow down safely, I most definitely will.
But if a small animal darts out at the last second in front of me, I am not going to react rashly to avoid it like I would a car or a kid. If the animal gets hit, it does, but I'm not going to risk my life or another driver's.
95% of the time, the animal avoids the car with me doing nothing but keeping on, I've only hit a couple animals ever. My guess is that by not swerving irrationally, I'm probably giving him a better chance of avoiding me than if I jerk the wheel in response, and I'm not endangering myself.
The one exception I do feel bad about getting run over is turtles.