The South should have won that war, actually. They won the initial battle and could have marched on Washington, but they were insistent on seceding, not conquering the north. That said, the North was unequivocal in its pursuit of keeping the Union intact. It was Lincoln's primary objective. Lincoln did care about the slaves, but not as much as he cared about preserving the union. This is why the North went to war, and it's what they "solved" by winning it. The country became one country instead of many after the Civil War.

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