All dogs bite it's the circumstances of the bite on whether it is a good dog or a bad dog. This is the message that I try to teach people in dog training classes; in the veterinary hospital where I'm a CVT; at the Safe Dog/ Safe Child Program that the kennel club puts for the area schools; and the 4H dog project that I volunteer at as a key leader. Man has taken this animal and domesticated it to live within a lifestyle that is foreign to it. Sometimes the animal might lash out due to fear, confusion, pain, training, and sometimes just plain viciousness. While I am against breed specific legislation I am for dangerous animal laws (lets not forget cats here). A bite is a bite be it from a rottweiler or a yorkshire terrier. The circumstances must be addressed. Lets say that a rottweiler bites someone who is breaking into your garage. Is the bite a good dog bite? How about the yorkie that bites a person who tries to pet it? Is the bite a good dog bite?
I can relate to the OP's position as I had the same horrible decision to make many years ago. I had a gorgeous Eng. springer spaniel dog. This dog was very nice and he was my first show dog. He was a show/obedience dog, did demonstrations for the local dog training club, and was very nice--except he had a secret. This dog had temperal lobe epilepsy AKA springer rage; intermittant rage syndrome. Five percent of the time this dog would have a siezure and he would attack anything; doors, dogs, me, people, fences, anything that was in his sight. We tried everything; anticonvulsants, behavior therapy, alpha training, drug therapy, castration. The only cure was euthanasia. This was a very difficult decision to make but one that I do not regret.