I believe that suffering is not the great evil to be avoided, but the means to joy—even a moment of joy can redeem decades of suffering.
Therefore, the number is ONE. Saving even ONE life is worth our societies enshrining complete prohibition of medical murder in our law codes.
Even rare instances in which new evidence exonerates prisoners decades after murder convictions shows that the death penalty ought to be outlawed. Likewise, rare instances in which patients, believed to be terminally ill, live much longer than thought possible negate the validity of the whole medical death enterprise. Furthermore, the experience of millions... perhaps billions on this planet who have, like me, undergone years of despairing thoughts and suicidal desires to develop more well-adjusted cognitive behavior undergird the ever-beautiful opportunity to stop the suicidal from self-murder in the hope that day will break once more.
I invite all who read this to come together in a culture of life that seeks to make use of and redeem all suffering, to engage in strenuous effort to overcome hardship, to take up "the life of toil and effort, of labor and strife; to preach that highest form of success which comes, not to the man who desires mere easy peace, but to the man who does not shrink from danger, from hardship, or from bitter toil, and who out of these wins the splendid ultimate triumph." (Theodore Roosevelt)
We ought to reject the idea that death is a proper cure for suffering, recognizing the ubiquity of suffering among all lifeforms, recognizing that there are no experiences so painful that no one has endured them without ultimately desiring death, and that, if we truly think that death is an appropriate cure for suffering, we run the risk agreeing with Silenus that "it is best not to be born at all; and next to that, it is better to die than to live", and, even worse, we run the risk of agreeing with him and losing the virtue of his hypocrisy!
People can make mistakes. The choice to kill a child or to kill one's self isn't always right just because it is chosen. In other words, people are not gods. You seem to agree and think it possible that something could go wrong here. But, have you considered that, if someone could be wrongfully "euthanized", that someone could be wrongfully left living? Out of the many faces you have seen in your life, are you willing to follow your moral logic through its full path and conclude that many of them should have killed themselves earlier, perhaps much earlier? How many people do you think go on making themselves live out of ignorant religious fear or compunctions that ought to be deprecated? If you really ponder these questions and those beyond, you may begin to feel the murky outline of the rough beast slowly, and sometimes blindly being conjured by the refashioners of moral taste.