Unfortunately for your argument, 'Bullshit!' and 'should be able to' appear nowhere in the Constitution.
What does appear is the following:
Amendment X
The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people.
Amendment XIV: Privileges or immunities, due process, elections and debt.
Section 1.
All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No State shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States;
Succession would constitute a law that would certainly abridge the privileges of the citizens of the United States (living in the succeeding states) by removing their United States citizenship entirely.
And, BTW, your marriage analogy is ludricrous.
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the fourteenth amendment was ratified in 1868, Trashie. you can not use it argue the illegality of the secession of the south.