No matter how you arrange the statistics, the South of the 1860's was agricultural. Practically every slave owner worked in the fields with his slave labor, while the children did the same.
This points out the absurdity of the Slave Aristocracy concept. However, you did assert the big fallacy that the South was fighting to preserve slavery. Remember, it did not have to fight, the slave states had seceded and specifically legalized slavery in these states.
The South fought to keep the armed people of Mass., RI, NY, Ohio, Pa., NH, IL., etc. off our land.
You should be asking why, if slavery was gone from the North due to secession, were these people were ordered to our soil?