When it comes to exotic animals, that's actually a very hotly contested topic that unfortunately has most of the information loaded on the negative side in regards to the animals themelves.
Time and again, people try to exotic pets with truly tragic results and this almost always results in negative publicity, to the point that for 95% of the population when asked "What kind of exotic animal can I get that's like a dog or a cat?" my stock answer is "a dog or a cat."
Many exotic animals may be imprinted at an early age, to make maters worse, to the point that they can also never be returned to the wild for once they have no fear of humans they are either destined to become dangerous to man or else to be horribly slaughtered when they approach a human, seeking a friend, only to be greeted by fear, terror and a mutilating or fatal attack in "self defense".
There is also one other fact and that is no matter what the laws, well intentioned people will still TRY to keep exotics meaning that , in the end, there have to be special people willing to live with the mistakes, willing to retrain them for release to the wild, or, worst case scenario, euthanize the animal if needs be, which is always sad.
As to diseases, yes, you can catch "parrot fever", a form of TB from your fish (both fresh and saltwater) and even fatal diseases, such as Nile fever are often vectored by exotic birds at first, followed by native species afterwards.
Any professional also knows that rabies can always be a hazard with mammals as the current vaccines for dogs and cats are almost always fatal to exotics, no matter what you've heard and even house cats can and do carry infections that can be hazardous if not deadly to pregnant women.