Oh, they used a perfectly good reason, but based on a badly flawed premise. The "good reason" was something protected by the 10th Amendment, powers not specifically enumerated in the Constitution being reserved to the various States, but the "states rights" had to do with the propagation of the institution of slavery. And a unilateral declaration that slavery was now an illegal activity elsewhere in the United States led to the secession of the South, as the Confederacy.
Needless to say, the attempt at secession was unsuccessful, and the old Confederacy was re-integrated into the Union, under force of arms. But even after being once more a part of the original Union, the seething resentment went on for well over a century, and the "reconstructed" states were held to be sort of second-class citizens, not politically reliable for the advancing civilization of the Northern states.
But now that "decivilization" has set in in several of the states, particularly the West Coast and portions of the East coast, the divorce of the civilized part from the now feral part of the country becomes increasingly a better and better idea.
I wonder if the confederacy had not supported Slavery then maybe the North would not have waged war. Hard to tell, but the north wanted to end the practice.