That assumes that Slavery was not a system that non slave holders supported or aspired to be part of. But really, as you suggest, non-slave holders were simply fighting for their nation, of which slavery was a fundamental institution. They weren't fighitng for slavery in the abstract, no. But you really can't divorce the South from the institution of slavery.
Do you have examples of letters or whatnot of non slave holders discussing why they fought? I think that would be rather interesting. Certainly all the top level political disputes, conflicts, and even battles leading up to the civil war were directly tied to slavery, but that is different than saying the average footman was fighting for that cause in particular.
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