My parents are reluctant to put our dog down?

My question is should I encourage them to go through with it? They have been considering the idea for a while and I think it is well past my dog's time. He's only 14, but he has lost the luster in his eyes. He sleeps the majority of the day and has sores all over from lying down so much. He has Cushing's disease (which causes weakening of abdomen and leg muscles and excessive thirst and urination), arthritis, and recurrent infection. He has poor appetite, never wags his tail and has great difficulty getting up and moving around. I pity him. But my parents don't want to let go. I love our dog, but he seems to be miserable.