In the Declaration of Independence, Thomas Jefferson established that people are endowed by their Creator with certain unalienable rights, and that governments are instituted to secure those rights. One right he specifically identifies is the right of the people to alter or abolish their government and create another that suits them better. This right both pre-exists and transcends the U.S. Constitution. How grotesque, then, that the only time Americans have attempted to exercise this right, the government that was supposed to secure it for them made brutal war on them instead.
You left out a key portion of his writing: “That whenever any Form of Government becomes destructive of these ends...”
There did not exist a form of government that was destructive to the ends of southern states in 1861 - unless you consider the southern states as self-destructive. The grotesqueness was on the part of the insurrectionists who made war upon their own nation..