Coexistence?

"How could both Sectionalism and Nationalism exist at the same time and at the same place?"

Sectionalism and Nationalism can coexsist in the same place just like how an Arabic person can reside in the States.
Everyone is "yaay for equal rights!", yet people demand that someone wearing a turban in the airport should be throughly checked for explosives.

They are contradicting terms, yet they were team players during The Era of Good Times.
While the south encouraged the use of slavery so that its economy could still thrive, other states began to become "free states". which spurred the south's need to become sectionalist. If they could diverse themselves from the rest of the country, they could continue to have slave labor.

Despite wanting to have slaves, the south also wanted to be involved in nationalism. The wanted the benefits of having a government not impaired by other world powers.
This sense of nationalism increased after the War of 1812. The sense of being an American enforced the want of nationalism.