Civil War: How to prove The Confederates were fighting for the right to separate from The Union....?

Ultimately just look at the prsidential election of 1860 for your answer. Between the 3 candidates, Lincoln got less than 40% of the vote (all Northern essentially) and wont the election over the 2 soutern candidates. That told the South that they would be dominated by the North in Congress and nothing they wanted would matter (like slavery for example)