That argument may hold some water in the Deep South, but Texas had less slaves than most, and yet still contributed 70,000 men to the Confederacy. I had an ancestor that was a cattle rancher, owned no slaves, and still fought.
Obviously, one would think there were more reasons at stake than slavery....
I don't believe hardly any of the Southerners who fought in the Civil war in any way believed they were flighting to protect slaverey. I don't believe hardly any of the Union troops believed they were fighting to free the slaves. In fact, I would venture a good number of Union troops were not happy with the Emancipation Proclamation and the belief that suddenly the war was about slaves. Slavery was at the heart of the sectionalism that divided the two regions and led to the war, but once war started it became about rights.