The colonists in the 1700s weren't about "self-determination." They had specific grievances with the crown and wanted a voice in making the laws and setting the taxes they'd have to live under. Only after fighting had started did independence become an issue.
The slave states were represented in Congress in the 1800s. They did have a voice in the government and a say in forming the laws they'd have to live under. They could have used that voice in Congress to renegotiate or to dissolve the union. Instead they decided to break away on their own and form a new country opposed to the US.
That was a spectacularly bad decision and different from what the colonists were doing during the Revolutionary War era.
You might want to look up the Morrill Tariff.