They wanted to overthrow the powers the Federal Government had over them. Revolution.
If you study history, you'd know they had that right. Again, the United States before the Civil War was like the EU today; a loose confederation of independent states. Historian Shelby Foote’s observation puts the difference very succinctly:
"Before the war, it was said ‘the United States are’—grammatically it was spoken that way and thought of as a collection of independent states. And after the war it was always ‘the United States is,’ as we say today without being self-conscious at all. And that sums up what the war accomplished. It made us an ‘is.’"
FWIW, General Robert E. Lee thought secession was a bad idea, but believed it was his duty to serve his country. His "country" being Virginia because, as Foote alluded in the quote, people in those days thought of themselves as Virginians, New Yorkers, Ohioans, etc, not as members of the United States.
I don't know your age, but I'm 69. Even in the 1960s, as an Army brat living across many of the States, many people still thought in terms of "I'm a Missourian" or "I'm a New Yorker" as opposed to simply believing "I'm an American" are more people do now.
Something else to consider is, 160 years later, discussions of the American Civil War are still heated and acrimonious. Only the fucking morons are arguing that slavery was anything less than an abomination. The argument generally centers around State's Rights vs. an all-powerful Federal government. With Trump in the WH, it appears you've won, Jarod: We, the People, are now getting an all-powerful Federal government. Congrats! LOL