The Constitution was adopted to REPLACE the Articles, not augment them.
The Constitution contains NO prohibition of secession. Therefore, Amendment X makes it legal.
Desirable? NO! A great idea? NO!
Legal? Yes.
The government is given the power under the Constitution to suppress insurrections which is exactly what Lincoln was dealing with. Armed bands of terrorists attacking US installations is an "insurrection" and Lincoln put that one down. No one need pay any attention to those attempting to defend and justify such insurrections even when glorified by the cockamamie concocted concept of secession.
There was no mention of this in the body of the Constitution because the concept was so unthinkable that the Founders NEVER once discussed it during the Convention. They ALL believed the Union to be perpetual.