Actually, as pointed out, the whole of the world didn't move away from slavery. It is still alive in much of the world. Africa, the Middle East, much of Asia still practices slavery. Unfortunately, we have a long way to go before we eliminate slavery.
In the places where slavery was abolished, it was almost without exception done peacefully, generally through compensated emancipation or through phasing out slavery over a period of years. And while the Psalms singers like to take credit for ending slavery, it was really simple economics that did the trick. Owning slaves just didn't pay. (We might as well face facts, for many people, if not most, money counts for more than morality.)
Don't think I am defending slavery or defending the South's stance on slavery. But this is not a question of whether slavery was right or wrong. There's no question that slavery is wrong. It is a question of whether people may decide what kind of government they will live under.
The point for our discussion, perhaps you will agree, is that those portions of the world making some serious effort to conform their practices to moral law and justice, i.e., Christendom, did eliminate slavery. And they did so as part of what Tocqueville identified as the irresistible force of the doctrine of human equality. The thesis of his book, Democracy in America, is that the tide of human equality was sweeping over the civilized world, and that rather than resist it, the old world should take careful thought how best to order affairs in light of it. I would be interested in what others who have read the history of this time would say about the thesis that emancipation in the British and French empires was entirely an economic phenomenon.
I think the point is that the South was unique, certainly among peoples tracing their political institutions to the Western or Christian civilization, in making a deliberate decision in the 19th century to embrace or defend slavery. In this, they departed diametrically from any society with whom they shared traditional or intellectual connection.