Actually the oath they take in medical school is: Do no harm.
I support Euthanasia, particularly on a personal level. I would recommend a book called, "Dancing with Mr. D." which is the accounts of a pallative care doctor for one year in holland (where Euthanasia is common) and examines a lot of societies attitudes about death. It was particularly poinant because I encounted a lot of these last month during my grandfather's lingering death. Particularly the attitude of his daughter and son that "he's suffering and should be put out of his misery" - while the reality was that by that time, he wasn't suffering, they were. And his lingering, gasping, 8 days of dying were torturing them, not him - which is insufficent reason to kill someone (because you are emotionally inconvienanced).
Now, while I have noted the above, I do believe in euthenasia as a form of pallative care, one which a person, in consultation with doctors, is able to go with love, choice and dignity. Personally, I don't know anyone in pallative care that doesn't feel that Euthanasia has some place in thier practice. This is because though we don't call it such, we already practice a "latent" form of euthanasia, known as the morphine drip. Which means that once your dying relative has been put on a level of morphine, they will peacefully go into a coma from which they will never come out. The doctor doesn't know when they will die when he/she "eases thier pain" but they know that it is a one way trip.
For my many friends facing degenerative diseases, they face them well, taking what life is offered as it is offered. But, even so, it is with the comfort that they will not have to lie in the body as a tomb, being unable to scream from the labouring pain as thier lungs and heart strain to continue thier function. Some will choose drug induced coma death, perhaps others more direct methods. I don't think anyone who has witnessed enough death up close and personal can remain objective or rejoicing in the plan of God which allows a persons body to literally rot away, or to die in agony over a period of months, unable to move.
I don't believe God is so jealous or controlling that God needs our every last scream and swear before we face God with a "What the **** was that all about you sick twisted diety?" - God gave us choice, brain, compassion - in my case and my partner's case, that's is the part of God we will be relying on - not some modern interpretation which would even rule Jesus's death a form of assisted suicide (he did walk knowing to his death, and did get a spear in the side).