I had a dog who was food aggressive, and especially with dogs, she never bit a human, but she would constantly attack our other dogs if they went to near to "Her" food. We had to rehome her, because she was out of control, and to much for us (She was a Lab/coon hound mix) I refused to take her to humane society because I was afraid she'd be put down because of her aggression. So we tried to train her out of it, she wasn't food aggressive with people anymore, just dogs. Humane societies won't put a dog down just because it doesn't get a long with other dogs, they will just rehome them to people who don't have any other dogs.
But, you say your dog bites? They will put a dog down for biting people... even fear biting. So your best bet is to keep him, or try to find someone who is willing to work with an aggressive dog. Because if you do take him to a shelter or a pound, he will more than likely be put down.