I think the issue is safeguards, so the decision to be assisted to die is the decision of the individual and not the decision of the family group or others who feel it is 'best'. If a person is of sound mind and can understand and make decisions (but has terminal cancer or other condition, which is why they want to be assisted to die) then that is fine. If a person has for example dementia, or has had a stroke, their ability to make those decisions is reduced or may not exist.
There is a season 1 episode of Star Trek voyager called Emanations that is themed around this sort of issue.