So said England about the colonies obtaining Independence. I think they were less afraid of anarchy, and more afraid that the Southern states would become the new base for Wealth and Power. I've pointed out many times how Southern independence was a dire threat to the money men of that era. (Later known as "robber barons." )
The Confederacy would have first absorbed all the border states and their markets, and it would have eventually absorbed all the territories too. The map of the Confederacy would have came to look like this for a time.
I would agree that parts of a country should be able to separate when the ability to choose one’s leaders is absent (taxation without representation) or by mutual consent.
How many southern states voted for Lincoln? I believe he was elected entirely on the choice of the Northern coalition. Same group that already had congress locked up.
The Southern states could do nothing to change their circumstance, and their circumstance was to serve as the milk cow for New York and Washington DC, through which all of their production money funneled.
I don't know about you, but most people wouldn't like being a milk cow for the Liberal parts of the nation.