I don't know if I would go as far to say that it is wrong to keep one type of an animal by it's self, but I do believe it is wrong not to have interactions with your pets. All animals in one form or another crave attention. Dogs and cats, of course. Birds like other birds to talk with, but will do fine if their owner spends quality time with them.
Rabbits kind of do their own thing but do enjoy company in the form of other pets. I have owned rabbits and they did ok together, but seemed to enjoy each having their own space. Horses enjoy the company of other horses, as do cows and sheep and pigs, etc..
So I guess most animals prefer companionship, but are willing to go it alone if their owner does his or her share of giving time and attention to the animals they own.