Sure it was about slavery as the wedge issue over which to decide whether you can leave the union. This sort of reactionary rhetoric just skirts over the surface.
It's not like the confederacy was fighting for slavery and to be part of the union. Both Kentucky and Delaware were happy with the status quo. The confederacy wanted both slavery and to leave the union, which they perceived to be their right.
The federal government at the time was much smaller than the current one and much less empowered.