We should just let people die naturally instead of killing them and "speeding up the process" as some would call it. Life is a gift and we must treat it that way. Euthanasia is dehumanizing and it makes us see people as a burden. We shouldn't make permanent solutions to temporary problems and we should accept all suffering and try to get something good out of it.
Nobody besides god should be able to kill and also it is basically just murder! What is wrong with just following the natural cycle of life?! Even patients who have severe problems and are dependent on life support should not die through euthanasia because the is ALWAYS hope they can get through it or at least live with it!
The bible may say this is wrong but it allows people who are going to die anyway in a painful way to get it over with quickly and painlessly. If you had a chance to skip to the end wouldn't you? I think it is fine as long as that person says they want it to happen.
We have a word for nonconsentual euthanasia: Murder. However, when such an action is expressly part of an individual's own wishes for themselves, it becomes then not an act of violence (in most cases) but an act of great mercy. It can be very difficult for a person employed in the profession of healing to comply with their patient's wishes when presented with such a request, but the medical profession is likewise a profession of easing suffering and a doctor should not allow their personal feelings to supercede the best interests of their patient(s).
First of all, your request must be approved by a council of doctors and other officials. The reason why this should be allowed is because there are patients that have a slim chance of recovering and live in pain for the rest of their lives, so why not let them have a choice of "pulling the plug". Take ALS patients for example, these patients live semi-normal for a period of time but in their last years they lay in a bed unable to move, open their eyes, or talk. It would be similar to being in a coma, and during this final stage they are in incredible pain as all their muscles and heart fail. Why not let them (or family) have the option to end the misery?