Good point. But I would argue that we refrain from killing each others because it's no longer in our best interest to do so. We can afford to feed everyone and give everyone a decent life without killing each other. Also saving people gives us a bigger pool of talented people and diverse genetics.
When we cannot give each other a decent life, we resort to mass killing (even today) - think of all the wars started due to hunger or ethnic reasons.
My point was that we are responsible for the safety and prosperity of each other, not any animal. We have no obligation towards the safety of some animal. Evolution tells us that we have to care about the survival of our species. And in certain cases, we will help animals but primarily where helping them helps us (for example, to maintain stable ecosystem).
As for dogs and cats, we use them for our benefit - we feed them, protect them, give them a good life for our own benefit - because they have evolved to make them seem cute and domesticating them makes us happy and gives us mental comfort. This makes them happy at the same time (but that's a side-effect, not the intended effect in most cases)