It need not be a rational, value judgement. Reasons for ending one's life may also be emotional in nature. Ultimately the choice should be their own, but differentiating between those who earnestly wish to die and the mentally ill, who should be protected and helped, is incredibly hard.
Euthanasia should only be allowed to those who have no options left, and even then the patient should be psychoanalyzed to make sure they are of stable mental health to determine if they should have the right to take their own life.
Only if the person has been checked out over years and is determined to be stable, and they do not have a place to function in society. It is more unethical to have blood on someone else's hands for killing a patient who could have had a chance at making any sort of successful recovery.
They should be made aware of all options since this is a medical setting. Here some options which are listed in US laws: "comfort care, hospice care, palliative care, and pain control." None of these laws say that patients should be denied lethal prescriptions because other options exist.