First of all, both the Articles of Confederation and the US Constitution are contracts -- intended to be "perpetual," and in Madison's word "forever."
Yes, it was considered by the Founders possible to desolve, but only through "mutual consent" or from "usurpations" and "abuses" having that same effect.
The Founders did not allow for secession "at pleasure."
And yet in 1860 there were no "usurpations" or "abuses" -- the Federal Government had not become "destructive of these ends".
The only difference between 1860 and, say, 1859 was the election of an anti-slavery Congress and President -- neither of which had yet taken office when the Deep South seceded, "at pleasure".
So the Deep South began to secede "at pleasure," then immediately to use force and violence against Federal properties and people.
That made it a "rebellion" and "insurrection," which the Federal Government is expected by the Constitution to defeat.
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This is a hand-wave based upon subjective criteria. The States that did the seceding obviously thought otherwise after considerable deliberation and argument. Hence, their grounds were every bit the same as those who signed the Declaration. Thus, empty hand-wave.