The two cannot logically be combined. Either secession was a legal and constitutional action, in which case it should have been handled by the appropriate legal and constitutional means, such as a lawsuit in the Supreme Court asserting the right. Given the composition of the Court at the time, there is every reason to believe such a suit would have been successful.
Or secession was based on the right of every people to revolution. But once one resorts to revolution and the sword, one by definition abandons all right to appeal back to law and Constitution.
You just can't have it both ways.
BTW, the right of revolution does not mean that others have no right to contest your right to revolutionize. Once you have appealed to the decision arms, you give up your right to claim that others have no right to fight back.
The seceding southern states chose an appeal to arms, on various assumptions, largely because they (correctly) assumed that fighting would bring Upper South states in on their side. Where they miscalculated was that it didn't bring (in the long run) the border states also in on their side. Had they been correct in this assumption (especially MO and KY) they would have won the War.
Other incorrect assumptions: The North was populated entirely by cowards who couldn't fight against southern gentlement. King Cotton would ensure European intervention and CSA victory. And a good many others. All of which turned out to be illusions.