There are some enemies in the compound who are sworn pets and would not normally associate without a healthy dose of convention. There are times of endless cat and dog fights which look irreconcilable. The interesting thing about these fights is that they rarely result in fatalities or even injuries when the pets are related thematically. But when the pets are unrelated, this results in a tragedy of sorts when the weaker pet is scratched and sheds some blood resultinog in the carnivore devouring the weaker pet especially if it is a chicken. There are some instances when a dog has to be contained in its kennel when avian pets are roaming about since after tasting blood, they seem to be impossible to rehabilitate.
I definitely do believe that certain pets should be kept separated from each other. Dogs and chickens are natural enemies, yet at times a dog will be protective of 'his' flock, assuming that he's been well trained and watched carefully. One must use discretion when allowing certain pets to roam freely together, and it's best that those pets be monitored during their interactions. A much better idea for chickens is to have a small flock of geese nearby as they tend to act as watchdogs, honking loudly and rushing at any strange animals that might pose a threat to the flock. In this way, I was able to keep chickens, ducks and geese together in the same run for years, without losing any birds to predation. Chickens themselves often cause the most damage to each other as they will spot something red, such as the wattle of another hen, and peck at it for hours until the poor victim is either gushing blood from multiple wounds or lying there dead. So in some cases, even when the pets are related, or of the same species, they still attack and kill each other. Pets of any kind are capable of hurting or killing each other if they aren't kept under control from time to time. I firmly believe that pet birds and cats shouldn't be allowed near each other without human monitoring, as some things are just common sense.
When we're talking about rivalries between pets, then I think we're all well aware that what we see on the cartoons isn't exactly how it works. Cats chasing mice, Dogs chasing cats is what we're used to seeing but rivalries between different animals is only natural I think, and in the past I've had a rabbit that's chased a cat around the garden so there isn't any set rules as far as I'm concerned.
All animals are protective of their surroundings so introducing a new animal into the home is always going to be a challenge no matter what they are, but with a bit of time patience and effort, I do think that most animals can get over the initial rivalry, and their inquisitive nature will take over. As others have already said though, sometimes common sense as to prevail and if you're getting a couple of budgies for example, it's probably better not to let them fly around when you've got a few cats on the prowl!
Rivalry among pets can be really intense. Growing up, my sister received a pet dog from her dad despite the fact we had two pet cats, who were litter mates and brothers. When we let them in the backyard, my sister's dog Pooh Bear would come and want to chase one of the cats. Without failure, the brothers would stick together and corral Pooh into the corner of the yard despite the fact he was bigger than both of them. Only when Pooh would attempt to bite did the claws come out. He was a smart enough dog that he only had to learn the lesson once. Mostly they hissed him into the corner. But Pooh was never allowed inside the house because it was the cats' turf. When he was inside, they would chase him into my sister's room. It was intense.
The ironic part was that the brothers had their own dominance games inside the house when there wasn't a dog. Drew, the older brother, was always the more out going cat. He was charismatic and would let almost anyone come and pet them. When strangers would come around the would rub on their legs before jumping onto their laps before receiving the attention he 'deserved'. He was the dominant cat. He would hiss and chase Tony, his little brother, into a crevice if he wasn't already there. He also had to sit higher than Tony. If Tony was sleeping under mom's desk, he was sleeping on her empty chair. If Tony was on mom's lap, he had to be cuddled on mom's shoulder. The only exception was probably in my room. I didn't let them on my bed because they were indoor/outdoor cats, so they had to stay on the floor. Because of this, Drew rarely came to my room. So, Tony usually hid out in my room, especially my closet.
We used to have a pigeon named Twinkle. She co-existed with our 2 dogs Tisoy and Epoy. When the latter passed away, we were given 2 puppies, Barbie the pekingese and Pipoy the pug. Again, Twinkle co-existed with the 2 puppies although at first, the puppies would be chasing Twinkle. And it only stopped when Twinkle got back at the 2 puppies. It's just sad that Twinkle left us after 5 years of staying inside our house.
We don't dare get another pet aside from a dog because Barbie is so ferocious. She's the youngest and only female so maybe she knows that she is our favorite that's why she bullies the 2 other dogs. I don't think Barbie would be amenable if we get another pet.