What are the causes of mercy killing?

Euthanasia or mercy killing in other words is a subject of much debate in the world. The idea suggested by it is that sometimes in case of an advanced malady or a crippling physical condition that the patient is suffering is not curable then it is ethical to rid them of their suffering. For example, the question that whether someone under life support who is brain dead, is it ethical for us to remove the life support and kill him when we know that he may never recover and be able to lead a normal life. There is always a high demand for medical care and it tends to eventually become too costly. So, when the case is that of an advanced terminal illness with no cure then is it appropriate to rid them of their misery? This debate has taken much force of late and is contested among medical doctors, with some for it and others against it.