I feel if you can meet the nutritional, environmental, and psychological needs of an animal and you have the proper training to be able to care for such an animal, then I say there shouldn't be a problem with you owning one.
The key word in the above paragraph is IF. Take a big cat for example. These animals are extremely dangerous and have very specific requirements. First of all, you must have a thorough knowledge of its nutrient requirements and be able to provide that. Environment is also another biggie with these cats. And that doesn't just mean giving it enough space to run. You must be able to provide it with a stimulating environment and above all, an environment that does not include human interaction. People think big cats are just that, big house cats and that is far from the truth. If you want to keep a big cat, you must distance yourself from it and limit human - cat interaction to a bare minimum, only to move the cat for habitat maintenence, vet visits, and viewings from a distance. People think they can go into these cages and play with their "pet" tiger. It just isn't like that and you will get yourself killed treating a tiger like a pet.
Now, does this mean no one should be allowed to have them, no. But the person that does keep a big cat needs to keep in mind, its not a pet, its a specimen, an animal you choose to keep to observe and care for, not interact with.