I see two large differences:
1. A requirement for euthanasia is usually that the patient keeps wanting it for a reasonably long period of time: it should never be a spur of the moment thing.
2. Another requirement usually is that the patient is mentally competent.
> When we hear about deaths, aren't the most painful ones those where a person has said "this human life is not worth living"?
If euthanasia is forbidden, people _will still be saying that in similar situations_, just they won't be able to do anything about it.
The differences you mention (duration of ideation/plan, competence) are ultimately about determining if the person "really wants to". But this applies equally to "normal" suicide: it places the many rationally planned suicides into the same class as euthanasia (it's their life, they're freeing themselves, keep your morality to yourself).
http://www.emorycaresforyou.emory.edu/resources/suicidestati...
Furthermore, according to the above link, of the 1 million who create a plan, only half report going through with it - how many with a "planned death" would not actually have gone through with it and instead endured, had they been lucid?
Should we be trying to prevent "(rationally) planned death", or shouldn't we?
* Is it because someone else performs the injection? Then what about suicide by cop, and cases where the patient injects herself?
* Is it because their family members join them in that initial feeling of peace following their decision (which suicide prevention pamphlets warn to watch for)?
* Is it because a cancer patient really is better off dead? Then so are many other seemingly-hopeless people, who are depressed, abandoned, and addicted. Is it because doctors agree that they are better off dead?
Nobody is pro-suffering, but sometimes we must suffer for the things that make us human. When we hear about deaths, aren't the most painful ones those where a person has said "this human life is not worth living"? No inanimate disease can say something so painful, can affirm it so permanently through willful action.