They appreciate it as perhaps no one else can. We do unfortunately see relatives of the terminally ill advocating euthanasia and assisted suicide. In other words, euthanasia is advocated by those who should be the care-givers and the supporters of the ill. It turns out that euthanasia is most strongly urged by those who stand to gain by someone's death. Ultimately, euthanasia is most strongly advocated for selfish reasons.
Death is an evil, except, it seems, when someone has something to gain by death.
Another approach is to reduce the argument for euthanasia to its bare essentials. In effect, those who promote death argue that certain problems make life not worth living. Certain problems, they say, cause suffering. Suffering is bad. Suffering should be eliminated.