Loving someone does not include murdering them.
So, when I put my dog down; that wasn't an act of love?
Consider, we are at war. I am captured. The Islamists are burning me alive, at the stake. There are 50 of them dancing around the bonfire at my feet. The fire is lit, and I'm being burned to death .
You are secreted 200 yards away with a sniper rifle. Do you let me scream and die slowly; or do you say a quick prayer, and show me mercy? Is that murder? How about if I cry out to you and say "Finish me"? Is that murder, or compassion?
In a very real sense, Dr. Kevorkian was in this scenario. So, would you let someone be eaten by flames, burned alive; or would you be merciful and take a single shot and end my suffering?