I grew up with a HA dog. We got a GSD puppy from a crappy "breeder". As a pup, she was fine. I remember taking her into my neighbors houses and she was great with the kids, even cats and dogs.
Unfortunately, we were way too dog dumb and inexperienced to handle a GSD, never did much of any socializing or training. I was 10yrs old and vaguely recall teaching her sit and down. Never walked her. She was too much for me and my dad was at a weird place in his life. So she just had the backyard. Anyways, she started turning very HA. We could not trust her at all. If guests came over, she would maybe pick one person she liked, and then pick another person to hate. She actually did bite two of our outside family members and the fact that she was sooo over-protective of me was NOT good. I couldn't even have friends over because she tried to attack one of them.
To be honest, I'm actually surprised we dealt with it as long as we did. But we really loved that dog, she was amazing with the family when it was just us, so I guess we just learned to live with locking her away when guests come over, etc. She was fine with other dogs but tried to kill our cat at the time so the two of them constantly had to be separated as well.
When she was 4 years old, a worker guy came to our house unexpected and Sadie, our GSD, was outside without us knowing (she was under the deck). She just went AFTER him. She could have done worse, he didn't need stitches but had a lot of puncture wounds. He legally had to call AC and well... they basically told my dad if it were to happen again, he would be fined or charged, etc, and gave him the option of putting her down which he sadly had to make. I wasn't home, thank God, but came home from school (first day of HS) to my dog just being gone. It was so sudden and I was in shock -- cried for days.
Anyways... long story short, I know my dad made the right decision. She was getting to the point where we just did not know what to do with her anymore and it was way out of our league. I don't think we could have just re-homed her to anyone, either. She wouldn't have done well, for the fact that she was so attached to me for one, and two, it would have been risky. In our case, I guess PTS was the right answer.
But, like, if she only didn't like certain things or certain genders, etc, I think it could have been controlled more. But she was unpredictable and that was the problem. If she had bit me once, let's say if I was trying to cut her nails or something, we wouldn't have been like "straight put to sleep right now!" or anything. I don't think one bite = death sentence.