Because the answer is very technical.
You are very correct. I may have misspoken. I generalized slightly when I indicated that euthanasia was a term that's well defined. It is well defined, but there are subcategories of euthanasia.
In the context of the Carter case, the court was only ever speaking of what could be called “voluntary euthanasia”, which involves the person who asks being competent to make the decision. They are aware of their circumstances; they have received the necessary medical information; and they are capable of understanding the consequences of the different decisions that they might make. In such a case, where a person requested assistance to die and they received that assistance from a physician, that would be called voluntary euthanasia.
It could be involuntary if, for instance, a physician terminated the life of a patient contrary to their wishes. That could be called “involuntary euthanasia”.
There is another subcategory that could be called “non-voluntary euthanasia”, which would happen when the wishes of the patient were unknown.
I thought it might be best to try to avoid some of these complications, but it turns out that it's impossible.
In the Benelux countries, they define euthanasia just as the voluntary termination of human life. In the European countries, where you see the term euthanasia used in some of the legislation, it means voluntary euthanasia. In pretty much all of the jurisdictions, physician-assisted dying is really limited to patients who have requested the assistance, who are mentally competent to make that decision, and who have been fully informed regarding their medical situation and the options available to them.
In the Benelux countries, it is possible for an advance directive for assistance in dying to be made, such that the assistance would be provided when the person was unconscious. However, the request would have been made when they were mentally competent and conscious.
The Supreme Court didn't deal with those sorts of circumstances. They really limited themselves to the situation where the person is competent when they make the request, and competent when the assistance would be provided. There are a few notable exceptions in the European countries, where physician-assisted dying can be provided under a slightly broader set of circumstances, but always with the request having been made by a mentally competent person.