My Catholic dogma may be out of date, but I'd suppose it goes as such: Euthanasia is de-facto suicide, and suicide is a mortal sin. Such sins may damn a soul to eternal punishment in Hell. Suffering at such intensity for eternity is much worse than the suffering at the end of one's life. QED, euthanasia is bad.

I'm certain that I'm butchering this. Also, to be clear, I am NOT advocating one way or the other on this reasoning, just giving what I can remember about the reasoning. Again, not my reasoning or advocation.

If anyone with a better understanding of the reasoning would comment, that would be great! Thanks.