Tough question. More complex, though, than we're letting our discussion of it be.
Do I believe people have a right to die? Dying isn't a right; it's a process we begin from the moment of our conception. It's a universal fate. It comes to everybody, wanted or not, and marks the end of that person's span. Ron's right about the semantics of the issue controlling so much of the discussion.
When I worked on locked psychiatric units I would get regular requests from some patients for me to bring them razor blades or poison or a gun so they could kill themselves. After all, I seemed like a reasonable guy, and any reasonable guy would understand that people had a right to die, didn't they?
I used to hate those people. Because, yes, I did believe that people had a right to die and their accusations, which generally came very quickly, that I was being a hypocrite didn't make things easier for me. I decided I would have to live with being a hypocrite for a while while I figured things out. The job was already getting me beaten up underpaid. Maybe hypocrisy was simply another job benefit.
After a long time sitting with my moral discomfort, I realized that I believed in people having the right to make a personal decision to die, and to carry that out if they had to. I didn't and don't like that decision, by the way, from having had to clean up after what some of these folks have left behind them. I don't believe their decision means that everybody around them must snap to attention and carry out the will of that person who made this decision I'm not terribly fond of in the first place,
I don't like you wanting to kill yourself, won't help you with your plans, and will do what I can to dissuade you. I have to live with myself, too, not simply with your demands that I help you do this thing I will acknowledge you have a right to do. If I were to love you enough to believe you, I would not be able to bear to pain of helping to create your loss. I simply not as noble and self sacrificing as so many others, who might be able to do it for you.
If it were a matter of physical pain, I would work to get you the right drugs, many of which are illegal in this country. When I've started an abstract and hypothetical conversation and come to the point that I'm using the second person form of address, I know it's time to stop.