Frankly I don't care if you believe it or not. I only honestly hope they none of your animals get to that point.
It's not about a terminal disease it's about chronic suffering. And yes, for humans as well im arguing for medically assisted suicide.
Your last point I don't get either l: How do you intent to help a German Shepherd with an infected hip who has a survival chance of 0% for an operation? How do you intent to "help" any being with an illness where no medication exist?
You sound to me like the "just work harder" equivalent of health.
You're full of strawmen to create a world that's just wrong because of the choices other humans make. Please allow a world that is just uncaring to all living beings - and some of us are confronted with that more than you apparently are. And no, I'm no longer talking about animals.