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I believe that the main motivation for the rebellion was the wish to preserve slavery.
It was clear that in 1861 Lincoln, an most Repbulcians. disliked it but did not see that they had the power to do anything about it in existing states.
There main point was to prevent this institution spreading.
Of course if Sessession had been accepted there would have been zero prospect of slavery being made lawful in new United States territories.
Did the CSA leaders seriously think that they were going to extend slavery in some other territories and that the United States would allow this?