The other side of that equation is the fact the patient’s life is being prolonged in the first place.
Prohibiting euthanasia is also prolonging life. Usually against the person's wishes. Sometimes prolonging an agonising or unbearable existence. Which makes it even more ethically suspect.
We are really allowing the resumption of a process that was already killing the patient.
Yeah, ok, so we can't kill a baby if we don't give it food. It's natural processes that killed it. And it's not murder if you switch off the life support of a critically injured person. It's just letting nature take its course.