This is a myth. Those men fought for their States whose rights under the Constitution of 1787 were abrogated by Lincoln and the other radical Republicans. The same goes for Robert Lee.
Dispelling this myth is important as the Constitution will no more protect your liberties today than it protected the rights of the citizenry 150 years ago.
Like many Cherokee, Watie learned not to trust the federal government- to the point of taking sides within the Cherokee nation on the question. In the end the abrogation extended to every facet of public life and the march of progressivism began. It is a sad story. And a greatly re-written one, with little caution for the facts, which are not remembered as myth.
How could Lincoln “abrogate” anyone’s rights when he hadn’t even taken office?
You are correct and I should have said states rights, for indeed, that is what they were fighting for.