It's not as simple as not wanting or not wanting to "play". You've said this several times and it is an uneducated argument involving no historical background.
Actually no I haven't. Its a simplistic argument rebutting your point that the South had some moral problem with the Union. It didn't. It was represented fine. It just didn't want to be involved for its own reasons. Call them slavery, a feeling of states rights, whatever.
But that in a democracy the minority doesn't always win doesn't make it tyranny. That is an absurd argument.