The Constitution obliges the states and the American people to regard the Constitution as the supreme law of the land.
In other words, if a state is to secede, its legislation in this regard is subject to review under the authority of the Constitution. By refusing to allow secession statutes to be submitted to this review, the seceding states violated the Constitution and the officers of those states violated their oaths to uphold that Constitution.
Moreover, the Constitution forbids states to enter into pacts with one another - and it is clear from the speed and coordination exhibited in the creation of the so-called Confederacy that the officers of states engaged in that criminal conspiracy had colluded with one another in contravention of the Constitution and their oaths to uphold it in that regard also.