Slavery was slowly going away everywhere. At the time the Nation seceded from the British Union and formed a Confederacy, all the Colonies were slave states. As time passed, states slowly shed slavery.
It was far easier in the North, because labor intensive work was less of an issue in that more industrialized society, but in the South it was virtually essential to their economy, the bulk of which depended on labor intensive agriculture.
I think the same social forces that were abolishing it in the North would have eventually done the same in the South. It would have just taken longer because so much of their wealth and production was tied up in the industry.
Abolishing slavery in the southern states of that time would be like abolishing fossil fuels in our day and time.
Sure, nowadays the wealthy North Eastern liberals are trying to force us all to do this without any rational consideration of the costs to the people heavily dependent on cheap fuel, but back in those days they were trying to do the same thing over slavery, and for the same reasons.
Banning fossil fuels is today's equivalent moral crusade, but it doesn't have the emotional impact they had with slavery, and so it's not going very well for them.