"...the rights aforesaid cannot be abridged or violated".
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Can you show us what the Federal Government did in 1860-61 to cause "injury or oppression", or "abridge or violate" any rights? Violations of those causing 'secession' are in Madison's words, simply another name for revolution, while secession in the absence of intolerable oppression is nothing but a violation of a faith solemnly pledged -- i.e. an illegitimate insurrection.
It was the retained right of the state in question to make that determination, as New York had written, 'the powers of government may be reassumed by the people whensoever it shall become necessary to their happiness'. It was their call.