Define harm. I mean, we are talking about people who are effectively in intolerable and uncureable pain, here.
And what if dying is a greater harm than staying alive in pain?
Who are we to judge, sitting in our comfortable armchairs?
Surely it's a persons duty, not the government, to value their life and decide what to do with it, even if that means ending it?
A person has the right to govern his own life, yes. But that doesn't make suicide right. And as a matter of professional integrity, no doctor should even entertain the notion of helping a person commit suicide. It cheapens life.
If a young person commits suicide, it leaves a gaping hole in the lives of all the people he knew. Why is this sort of suicide any different?
Ask anyone wanting to commit euthanasia. I'd guess they'd point out the difference between curable depression and the 'cry for help/attention' type suicide, and the fact their death is already inevitable, it's just a question of how long they endure substantial pain and/or debilitation. They'd probably also mention that laws allowing assisted suicide will inevitably have measures to ensure the patient (or victim, depending on your perspective) is still of sound mind to make that decision, is suffering a terminal condition, and is indeed in severe pain or discomfort.
The reason suicide is 'wrong' in the case you make, someone who's otherwise healthy, is because it's something that's avoidable; usually a consequence of mental illness or some tragic events. We view it as wrong because it's partly our fault if we fail to do something to prevent it (when it's someone we know). The hole it leaves is partly a consequence; in the case of a terminally ill and suffering patient (and the suffering aspect is key here), the friends and family already know that person is going to die, is going to suffer, and they have already mentally processed that.
I wasn't particularly sad, for example, when my grandad died a few years back because he'd been suffering badly; his mind had pretty much gone, his liver was breaking down and his skin had turned yellow.... basically, I was glad he wasn't suffering, because we knew long before there wasn't any hope for him.