Positive Reinforcement Only, doesn't exist.
I know, I know, that's not what you wanted to hear. It's not what society wants to hear. But I challenge any trainer to rewire a truly aggressive dogs behaviour, with only positive reinforcement. Then I will change my mind.
I do believe that it is our moral and ethical responsibility to begin with positive reinforcement. Always. With MOST dogs this will be more than enough, likely for the remainder of the dogs life, if introduced properly, at an impressionable stage of the dog's life, consistently. Good luck.
Now, before things get outta hand, I'm not promoting corrections, physical abuse or whatever deranged torture procedure you have concocted in your imagination already. I'm promoting real life. Real circumstances. And real changes. If putting an aggressive dog down is the answer, then I respect that, for that situation. I'm sure people don't come to this decision lightly, and I know for sure the law doesn't. But if someone comes to me with the desire and commitment of NOT putting their dog down, and trying instead to incorporate strategies into their life to make the dog's life comfortable and manageable, then I'm game for whatever it takes. Short of obvious abuse methods. I can't believe I even have to say that, but someone will inevitably come back with something along the lines of, "so you're like gonna beat a dog to make it stop biting, good idea." No. What is a good idea? Research. Then research again before you call yourself a trainer. Anyone can these days. But I find the ones worth your dime, are the ones that want to meet your dog first before they can even begin to recommend a training regimen. It's our responsibility as owners, and trainers, to look out for the best interests of your dog. If someone wants to start with harsh corrections, stop and think. And if someone wants to throw cookies at the problem, stop and think. We need to become open to the idea of balance. Balance within ourselves, and balance within our training.