At the time, loyalties were to the state first. There was a difference in belief regarding the extent of centralized power, and the south strongly believed the states should have more power to govern themselves (the 10th amendment wouldn't disagree with them). It could be viewed somewhat similarly to a block European countries leaving the EU today (though the EU hasn't amassed the central power of the US gov't at that time, yet).
That said, it makes litte sense for Nevada to celebrate the southern rebellion, other than the west being settled by people seeking a new life far away from that centralized power.