"Exotic" is technically any animal that is not a cat, dog, or common farm animal (such as a horse, cow, or chicken). Animals such as snakes, tropical fish, conures, foxes, skunks, servals, and tree frogs are all considered exotic pets.
Being that I am an exotic pet owner, I feel very strongly that it is not "wrong" to own an exotic any more than it is "wrong" to own a dog or a cat. Appropriate pet ownership is something that should be celebrated and enjoyed passionately. Pets make our lives worth living due to the joy, excitement, beauty, and comfort they can bring. There is something soothing about being able to care for an animal, and the satisfaction of knowing you are properly caring for an exotic is sometimes even greater due to the fact that many exotics have difficult husbandry requirements. To meet the needs of a difficult to keep animal is immensely gratifying for me.
All pet animals had their roots somewhere. All pets were once "exotic." It isn't fair to assume that people who want to keep snakes or birds are cruel, while people who keep dogs and goats are perfectly normal. Dogs are descended from the ancestors of wolves, who traveled in packs and killed animals for survival, and fought in the mud for sport. Is it therefore "wrong" to keep a pet dog in doors in a lavish home with plush bedding, simply because that differs from what they would experience in the wild? Is it wrong to confine a horse to a pasture and feed it every day instead of letting it roam for hundreds of miles across a vast expanse of arid terrain, weathering famine, floods, predators, and even lightning bolts? After all, that's what wild horses do!
Exotic pet ownership is right for responsible pet owners, just like dog ownership is right for people who understand and are capable of fulfilling a dog's required needs. There is little difference.