This is fascinating. I am not an American and have never studied American history. (The only things I knew about the Battle of Gettysburg before playing that game were that the Union won and somebody named Pickett conducted a charge up a hill that didn't go well. I don't even know where Gettysburg is.) I am, in fact, your hated enemy, a Briton! (Of old; by birth, Canadian.)
The explanation for the Civil War that had coalesced in my mind over time was that the South seceded to preserve their states' rights -- proximately, their right to maintain the institution of slavery (similar to how the Colonies revolted to uphold their citizens' rights -- proximately, their right to vote on new taxes). I would be interested to read any correction of this summation/simplification (as with all historical events, it is a simplification). If you could give a bullet-point list of the two to three most important reasons each side went to war, according to your understanding, what would they be?
I also found the comments interesting addressing the motivations and resilience of the soldier-citizenry at large. It has always seemed to me (without reference to the American Civil War) that states have an almost irresistible method of persuading men to fight for them, independent of the morality of the cause. While men will desert, sometimes in large numbers, a state that summons an army has one, and a general who commands an advance has it, until his men feel defeated -- regardless of whether they wanted to be there in the first place. Some bemoan the susceptibility of the masses to a politician -- beware the general! The people's obedience to him is almost automatic, without him even uttering a threat. It doesn't surprise me at all that Americans followed their leaders and fought for their 'home team,' to the bitter end -- from the rest of history, that seems the natural thing to do. (Not that this discounts their courage -- all who see battle must have courage to withstand it.)
Those are the thoughts of an outsider. Happy (belated) Independence Day to my estranged brethren, now reunited in comradeship.