Human rights always start with the right to live, which also appears in the right to due process, the right to pursue happiness, the right to property, indeed all other rights.
Human duties always start with the duty to protect another person's life, and probably the most well-known Commandment (of the Ten) is "thou shalt not kill".
Thus it requires two or three supervening claims about morality to come to the conclusion that for some other person, it is better for you to cause that person's death. I strain to come up with an example.
Suppose that death is wished by the individual, who is however incapable of causing him- or herself to die. Still, as that person's friend, traditional friendship demands that you strive to prevent your friend's death, notwithstanding the person's statements, presumed to be in bad judgment. And the Hippocratic Oath demands of doctors that they just don't do it, unless "harm" can be redefined such that a person is "harmed" when you don't kill somebody.
Or suppose that the board of directors of a hospital, doctors group, or insurance provider (or state government) attempts to adopt a practice of medical euthanasia under some stated conditions, they might relieve an individual doctor of the final decision. But this seems to contradict the US Fifth and Fourteenth Amendments, which grant all persons the right to due process, in which nobody may be killed without being found guilty judicially and so sentenced.
"Pulling the plug" on brain-dead patients is different, in that the patient has been acknowledged by the medical community to be dead in spite of the appearance of certain vital signs. Until this understanding is overturned somehow, there is not a moral dilemma here because the person is dead. The difficulty people feel is a result of our medical technology and the way it prolongs dying.
It seems to me that regarding suicide, there is actually little anybody can do to prevent the suicidal from determining their own path. But there is a strong social and moral resistance from helping such a person down that path, including our moral and practical statements against suicide.