Comparing a tropical fish to a human being is ridiculous. I love my fish and I love this hobby, but I would not put the fish on the same level as my family or my children.
Fish get culled, eaten, and killed every day. What do you say to people who feed their oscars feeder fish? How is one any less cruel than another? If you have a severely injured fish and you want to try and nurse it back to health, that's your business. It doesn't mean everyone would do the same if faced with similar circumstances. I had a female Laetacara dorsigera get destroyed by her mate and the caudal, anal, and dorsal fins never grew back. I kept her in a 55 gallon with grow-out fry. She learned to work with her disability, but she never really thrived again. If you're going to anthropomorphize a fish by comparing it to a human, then don't you also have to look at its quality of life? Eating and surviving is one thing but that does not mean thriving. If you're going to say it's cruel to put a fish down, don't you also have to consider that it could be cruel to let them struggle for the rest of their lives to find food, swim properly, etc.? Oscars have the potential to live 8 - 10 years, if not more. Is OP going to keep this fish for the rest of its life? If not, what will happen to it? Will anyone want it? There's always the chance it will be doomed to a 20 gallon tank in the corner of a pet store somewhere.
I think there are a lot of factors that people don't consider before making a knee-jerk reaction to threads like these.