“They are pointing out that the “Southern Slave holding States” are being oppressed. Is that untrue or something? “
Then “slaveholding” was pertinent to the “oppression”. In which case slavery WAS pertinent.
Parse meanings far enough, and you can prove anything you want to your own satisfaction.
If they had said "free states", you would have still said it was about slavery.
They identified the states with which the Federal government was intending to go to war. It was identification It was an adjective to describe the Noun.
Their objection was that the Federal Government was going to war against some states, and whether they were slave or free would have made no difference to North Carolina.
They would have sided with whatever state was being attacked by the government.