Am I the only one here who thinks that people should not be helped to die by state sponsorship at the first point of asking and for whatever reason that they feel like?
I'd be hard pressed to find anyone in support of having the right to die on one's own terms who doesn't also understand the need for diligent assessment and screening.
That's not really your argument, though. Or rather, that's not what people are objecting to. From what I can gather, you seem to want to limit the option to a very narrow set of circumstances that only includes severe pain and suffering. This is what people are calling into question. This is where your argument is weak.
Just think of all the people who have attempted suicide and failed, and then came out of or came to terms with their depression/problems to live happy fulfilling lives? I bet they are glad now that they were not successful in their attempt and that they wish that someone that had talked them out of their rather terminal decisions.
These are the kind of cases that would be screened for in any ethical and competent system. Rash decisions that could be turned around with a modicum of human interaction or cooling period. And that number is significantly diminished when you take away the people who engineered their suicide attempt so that someone could intervene, as a cry for help rather than a genuine and fully committed choice to end their own life. If a person really, really wants to end their own life, they will do so and there would be no way to stop them. At least those who are physically capable.