We were told in driving class for school bus drivers, NEVER swerve to miss an animal as you can cause more damage than if you hit it. We had a driver that slammed on the brakes to avoid hitting a cat running across the road and she caused a rear end collision.She was empty and she didn't get hit.
I did see one where a guy swerved to miss a deer that jumped out on the road and ran head on into a car coming the other way causing serious injuries to in both vehicles and the deer was still hit and killed.