I think the Archbishop is wrong, because I believe he is mixing up the concepts of suicide and assisted dying.
Suicide is open to everyone currently breathing in and out. It is a choice to end a life for the reasons only the individual understands, believing that although their body is perfectly healthy, and may last to a ripe old age, they wish to exercise their option to find peace in the only way they believe they can.
That is a universe away from facing a slow and agonising death which you know is going to come within the next few months, and will see you and your relatives tortured by a premature end which cannot be avoided, prolonged to its bitter and painful end with no respite, or prospect of making a decision to die now, in less pain and suffering, than then, when the suffering and pain are utterly unbearable.
If your job is to be an Archbishop, you spend your life distinctly apart from the rest of the world on two ways. In one way, your opinion is looked to for guidance by people who believe you are right, even when simply human fallibility means that on occasions you will be unequivocally wrong. In another way, you raison d’etre is to spend life pondering concepts of life and death, with your daily life devoted to little else.
Anyone who’s nine-to-five consists of thinking about life and death and god and evil and God and the Devil must develop a much deeper (and potentially seriously over-thought and analysed) point of view, but that does not make that viewpoint right – it’s still just a viewpoint.
And I believe it is a wrong viewpoint.