It's more than obvious from the article that the author is "not a fan of the Confederacy" - the statement was likely included to establish his Political Correctness bona fides with readers who value such things.
More importantly, anyone who suggests that the right of secession is "easily refutable" has never actually debated the matter. Several States explicitly reserved the right to secede when they ratified the then-new Constitution; Americans including Thomas Jefferson and James Madison recognized the right (explicitly or implicitly) in their public writings; early American legal references (including Tucker's Blackstones and Rawle's A View of the Constitution) clearly recognized the right of secession; and the Constitution as it existed in 1860 nowhere prohibited secession (and the 10th Amendment may indeed have reserved that right to the States and their people, as suggested by Senator Toombs of Georgia and likely others).
One may not agree with Jefferson and the others, but it is patently ridiculous to claim that the right of State secession is "easily refutable"; numerous respected sources from the period actually suggest the exact opposite. It is disappointing to see such "click-bait" on American Thinker - it used to be a good web site...
;>)
The question on whether a state may leave the Union or not is not really the question. If we agree that secession is not prohibited then it becomes a question on how secession should be accomplished. Walking out without discussion guarantees acrimony and conflict, something I can’t see the Founding Fathers agreeing to, Both Jefferson and Madison in their writings said that secession should be done with the agreement of both sides, those leaving and those staying. Even Rawle, while claiming secession at will was allowed, admitted that the individual states did not have the power to do so arbitrarily.
Our own founding document declares secession to be a right.