In a video released exclusively to Premier the senior Anglican clergyman said he felt he had to explain to his friends who were "very surprised" and "very disappointed".
"The first is the fact of pain," he said, "We have in this country one of the finest palliative care systems in the world, there's no doubt about that."
He added: "Never the less, in spite of that, people do suffer and many cancer patients experience excruciating pain.
"Secondly there's the issue of fear. People have said we're afraid of where the legislation might end up, it might lead to very vulnerable people being abused by very cruel and greedy relatives.
"But we can construct laws that are strong, that are resistant and I believe that the unintended consequence is a really bad way of opposing the bill."
Lord Carey announced he had changed his mind on assisted dying in July 2014 and said he would support legislation that would make it legal for terminally ill people in England and Wales to receive help to end their lives.
The bill he had backed didn't have enough time to progress through parliament before the election but has now been brought again by Labour MP Rob Marris.
It will go a vote in the House of Commons on 11 September. MPs will have a free vote on the issue, meaning they will not have to agree with their party.
Under the plans two doctors would have to independently confirm the patient was terminally ill and had reached their own, informed decision to die.
Many Christian charities have condemned the proposals and the current Archbishop of Canterbury Justin Welby previously said assisted dying was "mistaken and dangerous".
Lord Carey has now joined the Dignity in Dying campaign which has released the video exclusively to Premier.
He added: "To say that we are suffering with you is, in my view, a very poor argument indeed.
"There's nothing noble about excruciating pain and I think we need as a nation to give people the right to decide their own fate.
"In my view it is a profoundly Christian and moral thing to devise a law that enables people if they so choose to end their lives with dignity."
The Church of England said it could not support the bill and that Lord Carey was entitled to his own opinion but added that the current archbishop had been clear of his view.
A General Synod motion to oppose the bill was unanimously passed.
A statement from the Church said: "We believe that the Assisted Dying Bill has the potential to damage both the wellbeing of individuals and the nature and shape of our society.
"If enacted, the Assisted Dying Bill would put at risk many more vulnerable people than it seeks to help.
"Every person's life is of immeasurable value and ought to be affirmed, respected and cherished by society. This is true even when some people no longer view their own lives as being of any further value."
The Church is encouraging parishioners to write to MPs to express the opposition to the Bill.