Father refusing to euthanize dog

How would you deal with your senior father who will not put his dog down?

The dog is about 16 years old. It had developed alzheimers a while back. When it is awake, he paces in circles throughout the house. He never stops pacing, except to sleep. He also has major balance issues, and can't walk straight.

He is also deaf, and mostly blind. He walks into chairs and walls, sometimes falls down steps into another room. He also pees in the house.

When he was younger, he was a completely independent dog, my dad would leave him home alone when he went to work and the dog has a dog door so would eat and pee and sleep. It was never a problem.

Now, the moment my dad leaves his house, the dog whines/screams non stop until he is home. I think it's the alzheimers as he is basically in panic mode until my dad is home. He will leave him for the entire day which I think is cruel.

On top of all this, he's eating less and looking like skin and bones, he can barely stand up to eat or pee (has major balance issues), has had some seizures, and will never relax. The only time you can make him sleep is to hold him to sleep and then put him down next to you.

Am I overreacting to thinking it is cruel to keep this dog alive? I really don't think this is a good quality of life at all. I think my dad is putting it off because he knows it will likely be his last dog, and is refusing to accept the reality of the situation. Is there anything I can say to help? I brought this up a few months ago and he said he knows he will have to put him down by the end of the year. Well it is weeks into the next year, and the dog is not getting any better. I'm just frustrated seeing a dog suffer and I think it's selfish to keep him alive in this state, but maybe I'm not a dog owner so I don't understand?