If it's contradictions in the Highway Code that you're looking for then try these: -
1) Mirror, signal, maneuver, versus the emergency stop situation of animal crossing the road
2) You're expected to take into consideration whether your application of brakes on a stretch of open road would endanger the traffic behind you versus tailgaters who follow too close (and the myth that "it's always the fault of the car in front")
3) Not driving unreasonably slowly relative to the speed limit (impeding traffic behind you) versus not driving so fast that an emergency stop for people or wildlife cannot be performed without loss of control.
So, if you're being tailgated by a heavy truck and THEN a dog runs out in front of you, clearly your own (and your passengers') safety takes precedence and the dog loses out. I don't think there is a law which covers it though.