Whether or not they can leave the nation is, of course, the key issue. Several of the clauses suggest that the state can't simply leave the compact, which is the whole point of contention. The Constitution states that "This Constitution, and the Laws of the United States which shall be made in Pursuance thereof; and all Treaties made, or which shall be made, under the Authority of the United States, shall be the supreme Law of the Land; and the Judges in every State shall be bound thereby, any Thing in the Constitution or Laws of any State to the Contrary notwithstanding." This means that treaties, as well as the Constitution, become the "Law of the Land". Judges are bound to this "Law of the Land", "any Thing in the Constitution or Laws of any State to the Contrary notwithstanding."
The Constitution also says, "The Senators and Representatives before mentioned, and the Members of the several State Legislatures, and all executive and judicial Officers, both of the United States and of the several States, shall be bound by Oath or Affirmation, to support this Constitution[.]"
It is especially and morally problematic to insist they abide by that compact when they have reached the conclusion that the compact has already been violated when deciding that they must leave the compact. The decision is to leave the compact. All strictures upon them for abiding by the compact are null and void once they've left.
It is more morally problematic to assume that the constituent components of a nation or even individuals can unilaterally choose to leave a nation and abandon the laws and treaties of that nation. The Constitution contains mechanisms for addressing conflicts between the states and between the states and the national government, among them the Supreme Court and the Constitutional Convention.
The seceding states did not first violate the Constitution by refusing to uphold all treaties...no...they first seceded. Such a secession was a formality as the Constitution to which they had been sworn had already been sundered by the actions of the Federal Government.
In other words, it wasn't a matter of secession so much as revolution.
Secession was simply a means of formalizing the revolutionary right into a channel that ensures its popular legitimacy. Contrary to the false claims of some modern writers who attempt to construct a wall of separation betwee the two acts, the confederates made no effort to conceal their invocation of the revolutionary right. The Charleston Mercury famously announced this when its headlines read that the "Revolution of 1861" had begun.