This is something that owners of pets should be aware of then they get pets of different species. Some anmals will get along fine with a creature that is usually considered food for them; but most often , that does not happen.
There are many cute videos on youtube and Facebook that show a beautiful parakeet climbing all over a cat, and the cat seems to like the bird; but more often, the cat is only waiting for an opportunity to catch the bird and make a meal of it then to become friends.
You cannot blame an animal for killing and maybe eating an animal that is normally food for that animal. The owner has to make sure that the small animal is protected from the one who wants to eat it.
Some dogs can be trained not to chase and kill smaller animals; but even then, the owner should always watch and make sure that the smaller animal is safe.
Many years ago, we lived out on a small farm and had a milk goat, as well as two large dogs. The dogs never once chased the goats or even barked at them; but one night we came home from a late trip into town and found that the dogs had chased the poor goat out into the deep snow and then killed it.
I have no idea why those dogs killed the goat, since they had always been fine together the whole time.
So, even when we think we know what an animal will or won't do, it is always best not to take chances.