For some South Carolinians and others, slavery wasn't a problem. It was a solution to the problems of plantation agriculture, racial differences, and class conflict. Here's a little more on that.
Add the Industrial Revolution on top of that by 1860, and the chaotic Democrat National convention where the Southern Democrats were not seated, and the Civil War that followed, and that was near the beginning of the most chaotic period in American history--1869 to 1896.
I don't think it was that the Southerners weren't seated, but that they walked out. More here.
In the 1860s, most Northern voters and soldiers were still farmers. By 1880 or 1900 industry would be a lot more powerful, but a lot of people project this backwards to make manufacturing look more important than it was.
One of the most important industries was textiles, and textile manufacturers weren't particularly anti-Southern. They got their cotton from the South and had to think twice about anything that would disrupt their supplies.
One could argue that at a deep level, the conflict between the "industrial" North and the "agricultural" South was bound to lead to war. But the problem is why the Union had such great appeal to Northern farmers. Why did Middle Western agriculturalists throw in with the Northeasterners? Slavery was a big reason for the way the sections divided.
The population was in the north and middle states at the time of the ratification of the Constitution, so they viewed the Federal system as something they could control. Not a problem there. Georgia and other low population states were concerned that their voices would not be heard so the Senate was to be selected by state legislatures rather than popular vote and two per state regardless of population, and slaves were to be counted in a proportion for representation in the House although they did not have the vote. No doubt some of that feeling of the FedGov being 'theirs' was still present in the north by 1860.