The fact that these States thought they had the "Right" to declare their neutrality from a war that the United States was engaged in demonstrates that the States viewed the United States as a collective of individual independent states rather than one one solitary country. This was what was taught in the Constitutional Law classes of the major universities including West Point. It was one of the assumed rights under the 9th and 10th Amendments and had been declared many times over in several other states not in the south prior to the War.
It is the old double standard, Do as I say not as I do.