See #93. They felt they had roughly the same "long train of abuses" that the Colonies had when "seceding" from their political bond with Great Britain.
In all those issues the South had representation in Congress. In fact, the South had a disproportionate level of representation in Congress. For the 80 years prior to the rebellion they had influenced the government and its policies far beyond their population by controlling the White House, the Courts, the Army, and the Congress. What you're saying is that just because the South didn't have everything its own way then that was cause for secession. Kind of a 'taking my ball and going home' just because they struck out once or twice.