While there are various ways to define what it is for a pet to be exotic, I will focus on non-domesticated animals. Naturally, some of these pets do not involve much moral controversy. For example, keeping a tank of small fish seems morally acceptable—provided the fish are properly cared for. I am, for this short essay, mainly concerned with animals such as lions, tigers, bears, wolves, kangaroos, pythons, chimpanzees and other such animals. That is, animals that are wild and can present a danger to human beings. Also of concern are exotic pets that might pose no meaningful direct danger to humans but could be a danger to small animals or the local environment.
One obvious moral argument against allowing people to own dangerous exotic pets is that they are dangerous. Bears and tigers can easily kill humans. There is also the harm caused to ecosystems by escaped pets, such as the constrictors infesting my adopted state of Florida. This can be cast as utilitarian argument in terms of the harms outweighing the alleged benefits of having such exotic pets.
The obvious response to this argument is that non-exotic pets, such as dogs and horses, injure and even kill people. As such, the harm argument would also hold against having any pet that is a potential danger to a human. This response could be taken to entail at least two things. One is that all pet ownership of potentially dangerous animals should not be allowed. This would not appeal to most people, given the popularity of dogs. The other is that people should be allowed to have potentially dangerous pets, be the pet a dog or a bear. While this view has some appeal, the easy and obvious counter is that there are clear relevant differences between pets like dogs and pets like lions, tigers and bears.
While a domesticated animal like a dog or horse can seriously injure or kill a human, they are generally less dangerous and far less likely to attack than a wild species like a bear or tiger. After all, domestic animals have been (mostly) selected to not be aggressive towards humans and for other appropriate (from our perspective) behavior. So, while my dogs were good at biting, they were not as dangerous as a bear and never attacked a human, even when provoked. This is not to say that it is impossible for a well-behaved dog to turn violent. This is just to say that a well-trained dog is radically different from a well-trained bear or tiger.
While injuries caused by dogs are common, this is because there are so many dogs kept as pets. As such, even a tiny percentage of aggressive dogs will cause a relatively high number of incidents. There is also a reasonable concern about dogs that have been bred and trained to be aggressive. Such dogs present a threat to people and arguments can be made about restricting ownership of dog breeds that are alleged to be prone to violence.
Another obvious moral argument is based on the harms done to the exotic animals. While domesticated animals can do well living with humans (for example, my dogs have been happy living in my house—provided they got their runs and outdoor adventures), wild animals often do not do very well. Many who own exotic pets cannot provide the environment a wild species needs to be happy and healthy. There are also the concerns about medical care, proper exercise, diet and so on. As such, allowing people to own such exotic pets would often have negative consequences for the animals. Once again, the moral case against owning such pets can be made on utilitarian grounds.
An obvious reply is that domestic animals also have needs. As such, it could be contended that if the keeping of domestic animals is acceptable if they are properly cared for, then the same should hold for the exotic animals. This reply does have considerable appeal. After all, if an animal is properly cared for and is healthy and happy, then there would seem to be no moral grounds for forbidding a person from having such a pet.
The practical problem is that caring properly for such exotic animals is more challenging and more expensive than care for a domesticated animal. As I mentioned, my dogs have been happy living in my house and going on runs and expeditions with me. While medical care and food was not cheap, taking care of them was something I could easily afford. Exotic pets often present more serious challenges in terms of cost. For example, a tiger is very expensive to feed and one should not take a tiger out for an adventure to local dog park. However, with proper resources these challenges could be addressed.
As a final moral argument, there is the concern that it is simply wrong to keep an exotic animal as a pet. To steal from Aristotle, it is not the function (or nature) of wild animals to exist as pets for humans. While people and animals might form bonds, the wild animals are such that being made into a pet is a distortion or even violation of what they are, which would be wrong. This, of course, would seem to suggest that we have distorted animals and perhaps wronged them by domesticating them—which might be true.
This line of reasoning can be countered in various ways, ranging from arguing against there being such natures to religious appeals to the claim that humans were given dominion over the animals and thus we can do what we wish with them.
My own view is somewhat mixed. Since I have shared my home with many dogs and cats, it should be no surprise that I am morally fine with having a pet (provided they are well cared for). However, I think keeping exotic animals as pets is morally problematic. That said, some people do truly love their exotic pets and take excellent care of them. In the case of endangered species, there is also the added moral argument about the preservation of such species as pets—which does have some appeal when the alternative is extinction. This does, however, raise the moral issue of whether existing as pets (or domesticated animals) is morally better than being extinct.
In closing, I would certainly not have a lion, tiger or bear as a pet. A dire husky…well, sure.