The states created the federal government, and the states can dissolve the federal government. That’s not at all the same as saying that any state has the authority to secede unilaterally.
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There are differing opinions. I'll present mine, then after work...I'll respond to yours.
St. George Tucker:
...Consequently whenever the people of any state, or number of states, discovered the inadequacy of the first form of federal government to promote or preserve their independence, happiness, and union, they only exerted that natural right in rejecting it, and adopting another, which all had unanimously assented to, and of which no force or compact can deprive the people of any state, whenever they see the necessity, and possess the power to do it. And since the seceding states, by establishing a new constitution and form of federal government among themselves, without the consent of the rest, have shown that they consider the right to do so whenever the occasion may, in their opinion require it, as unquestionable, we may infer that that right has not been diminished by any new compact which they may since have entered into, since none could be more solemn or explicit than the first, nor more binding upon the contracting parties. Their obligation, therefore, to preserve the present constitution, is not greater than their former obligations were, to adhere to the articles of confederation; each state possessing the same right of withdrawing itself from the confederacy without the consent of the rest, as any number of them do, or ever did, possess.
John Taylor of Caroline, a ratifier for the State of Virgina:
In the creation of the federal government, the states exercised the highest act of sovereignty, and they may, if they please, repeat the proof of their sovereignty, by its annihilation. But the union possesses no innate sovereignty, like the states; it was not self-constituted; it is conventional, and of course subordinate to the sovereignties by which it was formed.
The deputations by sovereignties, far from being considered as killing the sovereignties from which they have derived limited powers, are evidences of their existence; and leagues between states demonstrate their vitality. The sovereignties which imposed the limitations upon the federal government, far from supposing that they perished by the exercise of a part of their faculties, were vindicated, by reserving powers in which their deputy, the federal government, could not participate; and the usual right of sovereigns to alter or revoke its commissions..