Here is the view of the Christian Medical fellowship, and is part of a longer article giving twelve arguments against euthanasia. Note: not all Christians accept this view.

Source: http://www.ethicsforschools.org/euthanasia/twelve.htm

Voluntary euthanasia changes the public conscience
The law is a very powerful educator of the public conscience. When a practice becomes legal, accepted and widely practised in society, people cease to have strong feelings about it. This was most dramatically demonstrated in Nazi Germany. Many of those involved in the euthanasia programme there were doctors who were motivated initially by compassion for their victims. Their consciences, and that of the society which allowed them to do what they did, became numbed. The testimony at Nuremberg of Karl Brandt, the medic responsible for co-ordinating the German euthanasia programme is a chilling reminder of how conscience can gradually change:

‘My underlying motive was the desire to help individuals who could not help themselves… such considerations should not be regarded as inhuman. Nor did I feel it in any way to be unethical or immoral… I am convinced that if Hippocrates were alive today he would change the wording of his oath… in which a doctor is forbidden to administer poison to an invalid even on demand… I have a perfectly clear conscience about the part I played in the affair. I am perfectly conscious that when I said yes to euthanasia I did so with the greatest conviction, just as it is my conviction today that it is right’.[4]

He sincerely believed he was innocent. This demonstrates that once doctors start killing, it is possible for them to carry on doing it without feeling any guilt.