Public school education: very little on the Civil War was taught, just the most cursory of overview. I learned most of my knowledge of the war in college or private study.
The Civil War is second only to the Revolutionary War in importance for American history, IMO. The Revolutionary War set the parameters for what the United States could be; the Civil War defined what it would be.
The issue of slavery was the 'key' issue, but was not the only one. Underpinning the slave question was the notion of state vs. federal power..or the old 'state's rights' question. It was also the defining moment for what would be the primary political block in the nation; previous to the war it was the agrarian South, with Viriginia as it's center. After the war, the center of power shifted north to the Northeast and the industrial/financial busineeses -- areas traditionally more statist than the agrarian South, which was more individualist.
Underestimating the cultural differences between the North, South, and the West (not including California, which is extraterrestrial, politically and socially) is a common and serious problem in the US political and social debate. The legacy of the state's right movement held on through the Dixiecrats of the 1940-50s and continues today in the burgeoning libertarian movement. There is a sharp divide that was brought out particularly in this past election; the more rural/suburban south and midwest votes differently, has different values, from the more urbanized states of the East Coast, the West Coast, and the Lakes region.
In some ways, the Civil War is the precursor to all the issues of state vs. individual, gov't vs. business, gun owners vs. gun abolitionists, secularists vs. Christians. If anything, the divide grows sharper as the urban areas strive to increase control over what people throughout the nation, not just their areas, can and cannot do. The increase in political manipulation to create race issues in the past decade or so has also exacerbated the split between these elements of American society. There is an underlying homogeneity in the American culture that has been attacked by deconstructionist elements in the nation; these forces differences are causing a schism in US society.
The South may not rise again...but their issues may soon.
"War is an ugly thing but not the ugliest of things; the decayed and degraded state of moral and patriotic feelings which thinks that nothing is worth war is much worse. A man who has nothing for which he is willing to fight, nothing which is more important than his own personal safety, is a miserable creature and has no chance of being free unless made and kept so by the exertions of better men than himself."
John Stuart Mill