When the one party left, they took with them things that belonged to the "union" and they took it by force. So it's not like they were innocently just wanting to leave and had the north let them leave nobody would have been hurt. That's why the marriage analogy falls short - at least in the simplistic form it was presented.
I agree that we need critical thinking about the civil war, but there are some things that are very clear. The civil war would not have happened if either: 1) The south didn't have slavery or 2) the north wasn't interested in abolishing or at least preventing the spread of slavery. Period.
So while many parts of the civil war are nuanced and complicated (exactly what rights do the states have, should slavery simply be contained or abolished, what was the expectation of the founding fathers, how much force can a union use against its fellow members, do emancipated slaves have rights, etc) the central issue is not that complicated. Slavery was the driving force.