Having interacted with advocates of euthanasia, I remain unconvinced that it is a practice worthy of human beings and any society that can call itself civilized. I hear arguments of mercy, respect for autonomy, and the like, and I understand them. But I remain against euthanasia - strongly so - until the following questions be resolved.
First: How does one respect autonomy by destroying it? Euthanasia erases any possibility of autonomous action after it is administered, because the autonomous person will be dead. Dead people are not autonomous. (The living who administer euthanasia, however, go on living autonomous lives, and where it is legal, their autonomy is not hampered by the law.)
Second: In like manner, how does one claim to alleviate suffering when one ignores the suffering itself and instead ends the sufferer? When the person is dead, yes, the suffering is gone - along with autonomy, by the way - because the person is gone. I guess that's a way to cure the common cold, too, right? OK, that's a little flip, but the principle is the same: It is not a treatment for the disease when one kills the person who has the disease. In fact, the person himself is treated like a disease, by the living who administer the euthanasia, who by the way unlike the patient continue to live afterward free of the patient's suffering.
Third: How does destroying a thing reflect how much one values it? The comparison to animal euthanasia is often made. And while a family would love to have a beloved family pet continue to live, the fact of the matter is that euthanizing it is not only about the suffering of the pet. Believe me, I do get this, I understand. But... deep down... it is also about the value of the pet to the family. As beloved as the pet may be - when healthy - it does become valueless when dreadfully sick or injured, and there is no value in keeping it alive. If there were value in having a sick pet around more than euthanizing it, there would far less animal euthanasia, too.
Fourth: There is the meaning of suffering. Is suffering intrinsically meaningless? Does it have meaning "only if" the sufferer gives it meaning? Is it really a matter of choice?
Especially regarding the last question, but pertaining to them all, I think I know the unspoken premise behind these arguments. Even so, they are not necessarily compelling because they still look like logical contradictions - but they make more sense at least only if... well, I'll let you figure it out.