I back this up. There is a state well studied in animals called hopelessness. Animals of diverse taxa can and will develop depression-related or depression-like behaviours and even self harm, not even necessarily at an old age. The same logic OP uses to question euthanasia is the one we use to understand them and make decisions. We know they will not communicate as humans, and we know we are directly responsible for their (pets) quality of life. This creates the consensus that we have to infer their emotional state and assume them capable of suffering based on their physiology. This (through studying their physiological and behavioural responses) is how we learn for example that dysplasia can be very painful, or that lack of certain standards of care can cause immense suffering. For humans we have the big problem of Christianity, that permeates western notions and confuses morals with ethics, stating that all life is sacred and god intended your suffering for some divine purpose. So much so that suicide was considered a crime and would ban you from heaven. But in more developed places the idea of self requested euthanasia is slowly being better understood.

We don’t have a “right” to do so, we have a “responsibility” to give them the best we can provide.