Please read this:

The new Constitution has put at rest forever all the agitating questions relating to our peculiar institutions—African slavery as it exists among us—the proper status of the negro in our form of civilization. This was the immediate cause of the late rupture and present revolution. Jefferson, in his forecast, had anticipated this, as the "rock upon which the old Union would split."

He was right. What was conjecture with him, is now a realized fact. But whether he fully comprehended the great truth upon which that rock stood and stands, may be doubted. The prevailing ideas entertained by him and most of the leading statesmen at the time of the formation of the old Constitution were, that the enslavement of the African was in violation of the laws of nature; that it was wrong in principle, socially, morally and politically.

It was an evil they knew not well how to deal with; but the general opinion of the men of that day was, that, somehow or other, in the order of Providence, the institution would be evanescent and pass away... Those ideas, however, were fundamentally wrong. They rested upon the assumption of the equality of races. This was an error. It was a sandy foundation, and the idea of a Government built upon it—when the "storm came and the wind blew, it fell."

Our new Government is founded upon exactly the opposite ideas; its foundations are laid, its cornerstone rests, upon the great truth that the negro is not equal to the white man; that slavery, subordination to the superior race, is his natural and moral condition.

This is an excerpt from "The Cornerstone Speech", given by the Confederate Vice President Alexander Stephens. Its full text is in that link.

There you have the Vice President of the Confederacy admitting proudly that the secession movement was predicated almost entirely on slavery, and the growing abolitionist movement in the northern states.

It wasn't a rebellion against "bigger government". It was to maintain the unjust, undemocratic, and ultimately profoundly unAmerican institution of slavery.