Thorn69,
You are assuming the South had the right to secede, the federal government did not recognize the right of the rebel states to leave the Union unilaterally. They viewed that action as illegal.
If the Southern states really wanted to assert or confirm their legal right to withdraw from the Union, the proper channel was to the US Supreme Court which is the final arbiter of the meaning of the Constitution
so yes, you are right that the immediate cause was whether the secessionist states had the right to leave, but that begs the question, why did they leave in the first place? It was because they were worried that the election of Lincoln as president would endanger the institution of slavery.
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