So in general I think euthanasia is for people that live in deep suffering with no prospect of getting better. If you are asking a doctor to take your life, there should be a very good reason for it - that's just my opinion. The prospect of getting better is relevant, because the decision is so final. If you take a physically healthy persons life, you have no way of knowing if that person would be happy five years down the line. And if that's possible, it is inherently worth protecting in my opinion.
With mental health, I think it becomes a lot less objective to establish the extent of the suffering for a person. Disorders of the mind are in general just a lot less objective than physical ailments. A psychatrist will need deep understanding of an individual through years of councelling to be able to make a determination. How does that psychiatrist maintain an unbiased opinion? I'm not sure. Is it possible for the psychiatrist to shape the wish the patient (knowingly or unknowingly) throughout that process?
To me there seems to be a lot of uncertainty, and therefore, I would generally lean towards not taking a life.