Well that's wrong on every level. The south wasn't after Washington DC. They didn't seek to overthrow the government. They set to establish their own. Next...
As Town said, this isn't responsive to my point. They were trying to overthrow the governments...of Kentucky and Missouri, and replace them with new governments that would join the Confederacy, which in itself disproves the contention that they were motivated by concern for states' rights. The fact that they didn't attempt to conquer the whole Union is hardly relevant, and could just as easily be a reflection of strategy as anything else.
The Confederacy understood itself to be an institution dedicated to the preservation of the institution of slavery. In those terms, the invasion of these states made perfect sense. Both had large slave-holding populations, thus it seemed natural to the Confederates to take them to protect the institution from being snuffed out by a newly-abolitionist Federal government. But it makes no sense if the main cause was states' rights.