Where did you get that quote? It's not from the Declaration.
For the South, the reason for secession and the formation of the Confederacy was the protection of slavery.
That is just one assertion, and an unproven one at that. Beyond that, there are no conditions regarding the right to independence, else it would have applied to the original 13 slave colonies as well.
Was that adequate and proper cause to repudiate the Constitution?
The Constitution is not repudiated by states exercising their rights.
That is why, after the Civil War was over, Southern apologists contrived all sorts of evasions and excuses for secession other than slavery.
So you tell me, all the while ignoring the evidence of their constant economic complaints going all the way back to the 1820s.
Again, referring to the Declaration of Independence as the source of a right of secession stumbles on the fact that the Declaration affirmed that “all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.” Such a concept is inimical to slavery.