Jake's Story
I feel for your situation, I too have an unpredictable rescued male boxer. Jake came from a family that had no time for him. He was kept in his crate nearly 24 hours a day, never socialized around other dogs, and may have been otherwise abused. We have had him for nearly a year. It took him almost 3 months to settle in to our home, when he did he seemed to change dramatically. At first he was timid and seemed to accept most situations, including other dogs and the dog park. One day he got in to a vicious (in my opinion) fight with a pit at the park. Remember that drawing blood is NOT the definition of a vicious dog fight, if neither dog needs stitches it was not a serious as YOU think. Since Jake has become more comfortable with us, including our boxer girl Peach, he has become more protective/dominant over the house, and more unpredictable when we are out. This by no means makes me want to put him down, quite the contrary. It makes me want to do better for him than he had before. He is an awesome dog at home and is great with Peach, but I am always watching him just in case. I do not allow anyone other than myself or my husband handle him for any reason and we don't go to the dog park anymore. He is never off leash when we are out, even if there are no dogs around. All of these measures are inconvenient, but since he is unpredictable they are necessary. Difficult dogs do not need to be put down, you just need to be prepared for unpredictable behavior and predict problems before they occur. A basket muzzle might give you the piece of mind and the confidence needed to deal with his behaviors with out the fear of injury. Most dogs get used to them and they can pant freely and even eat and drink with them on. A rescue dog deserves every chance that you can give him. Only when you have exhausted EVERY possible mechanism for coping with his behaviors, should euthanasia be considered. It might be a drag to keep him home from the dog park, or employ a professional to sit while you are away instead of your family. But ask yourself if he is worth the extra trouble. True aggression in dogs is rare, most likely his problem is behavioral which if it can't be corrected, can at least be managed. Jake has never shown agression towards me or my family, but I am always aware of his background and his potential. This keeps me constantly aware of his body signals, just in case. I hope you reconsider, it sounds like you are getting bad advice- especially if given by people who have not met the dog in person.
Kisha