It doesn’t deserve denigration, but the con-fed’s bastardization of it does. The key phrase there is “That whenever any Form of Government become destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government...”
The government of 1860-1861 hadn’t “become destructive of these ends”. The slavers tore the government apart because they had a tantrum over losing an election. Sound familiar?
I think that is entirely in the eye of the beholder. George III thought he was perfectly reasonable with the colonists. The Colonists did not.
I think the Confederates probably didn't like the fact that their 1/4th of the citizens were paying 3/4ths the cost of the government, while at the same time New York Shipping, banking, warehousing and insurance industries were siphoning off about 40% of their profits.
In their eyes, the government had become contrary to their best interests and therefore "destructive of these ends."
That is no more important, no more “key”, than the phrase “as to them” shall seem most likely to effect their Safety and Happiness.
A state does not have to have permission to declare independence - that is the reason it is referred to as a Declaration of Independence.
A more logical argument, from your point of view, would be to say the Confederates didn't know what they were talking about because the Confederates were only the sons and grandsons of the founding fathers and never had the opportunity to learn history in public schools or watch television.