I am a little split.

Okay, true story, I am a long term dog owner that has once owned a mix that bit. It SUCKS. I've also been bit by a dog. Not my dog, a separate dog. My little sister took a good bite in the face recently. And I am not judgmental. So here me out.

You are both right, you are both wrong. This dog might be a dog you could save. Not having him around other people might be a reasonable solution. If there is company, the dog goes to a safe space. He can't be trusted. Or, he wears a muzzle. Then, with years of rehabilitation, he might be brought back (in small, tested increments) to be around more people. He could still have a happy life. When you talk about "surrendering" a dog that bites, you're talking about killing him. Don't pussy-foot. You can take him to the vet or the shelter can, but that dog is being put down. He's dead. That's the end of it, unless you lie and claim another reason. But even then, he'll show his true colors and that will be the eventual fate. You're talking about killing this dog, not getting rid of it.

On the other hand....so what? There are a million dogs in shelters that need homes today, not yesterday. You happened to get a biter. He's not safe to be a family pet. You tried to do the right thing and get a rescue and the rescue you got isn't in the shape required to be a family pet. It isn't his fault, but it is not your fault either. You didn't have the puppies, leave them up for grabs, and neglect the training that caused him to be a biter. You walked into a no-win situation and you got a dog that just isn't going to be the happy, family pet that people want. Rather than leaving him to years of loneliness, neglect, and sadness, you end a life that would never take off. It is sad, but it is what needs to be done.

There is no good solution.

So, what would I do? I'd muzzle the dog. Muzzle the dog outside the home and any time there are guests. Keep using the trainer. Keep trying to bring peace and calm to the animal, lest you end his life. Let your boyfriend wear down in the event that rehab isn't working so you can make the call together. He's not ready to give up on this life yet, so let him try. But, in the mean time, limit the liability such that the dog isn't a direct danger. Biting behavior still happens in a muzzle, but it doesn't cause damage. This way you can track his progress around people without putting them in danger of a dog bite. Revisit the issue in three months. See where you are. Re-frame the issue to be about the dog's happiness (never allowed to socialize or be outside without us being fearful. Never allowed to be a full dog because of his agression) with your fear of the biting. Talk about the long-term happiness of this animal if the only creatures he connects with are the two of you. Hopefully either the dog heals or your boyfriend sees the inevitability of the situation. No matter what happens, you prevent the dog from harming others.