Let's respond to this question through the eyes of the family caring for a sick or dying loved one, because that is the context in which most of us face this agonizing issue.
We do not like to see loved ones sick, dying, or in pain. It goes against nature, moral training, and Christian faith to sit happily by when they suffer.
Our first instinct will be to try to find a way to save their lives. We will be supportive of aggressive treatment for as long as our loved one, the rest of the family, and the medical team hold out hope for a cure.
When such hope is no longer realistic and death is imminent and certain, we try to make our loved one as comfortable as possible. There will be little debate that even if the family ends now-futile medical treatments (such as chemotherapy), all reasonable efforts must be made to alleviate suffering. Beyond hoping for a miracle, all who love the dying person will pray for a peaceful death soon.
So far, so good. The question, however, seems to presuppose that this strategy is not good enough when the dying person is in "terrible pain." At that point, it is implied, Christians are hardhearted in not supporting euthanasia.
This is a widely held view today. But it is wrong.
First we need to define some terms. Most thoughtful bioethicists or physicians accept the legitimacy of withholding or withdrawing medical treatments when they are no longer bringing benefit to an irretrievably dying patient. Nor is there any opposition to aggressive use of painkillers and other forms of palliative care.
But euthanasia is a different thing when it means (more than simply withdrawing medical treatment) ordering or implementing some act that kills a dying person: whether it is a lethal injection, an overdose of drugs, ...1