I don’t think you’re an asshole for yelling at the kid. But you should apologize for any names you called her. It was not your job to explain the situation to her, it’s her parents. My son is 6 and 3 dogs he’s had since birth have died, 2 were euthanized. By 5 he knew that dogs sometimes had to be put down, it’s sad, but it saves the dog from being in a lot of pain for even longer and they can be happy again. It’s that simple to explain. I was told the dogs to go heaven, I just told my son that they’re no longer in pain and happy now. At 10 I knew dogs had to be euthanized. By that age I had had classmates come to school upset bc their pet had to be put down, by 10 I was one of those kids myself. She knew better. But you should still apologize for calling her names. So I’d say ESH, the parents and girl more so than you IMO.