House cats prefer to chase birds, squirrels, and mice, not be chased by them. A chihuahua’s natural prey is often too big for it to catch; thus the little dog will avoid chasing pretty much anything unless provoked. Unlike a cat which hunger strikes if it doesn’t magically appear something at mealtimes, a chihuahua will pick up scraps of food from the kitchen floor if they pass by unnoticed.
Speciesism can also play a factor in whether or not two species are compatible with each other– just because they may live peacefully next door doesn’t mean that their existence impacts one another beyond what would happen without them there…