These two groups were conceiving of freedom in different ways. To Northern abolitionists, freedom was something that applied to all people. They felt that freedom precluded having the people of one race enslaving the other. But this is not the only way to conceive of freedom. The South felt that freedom could be defined as the freedom to have whatever economic and social system they wanted. They felt that freedom included the freedom to own slaves. This was the freedom to rule themselves in any way they saw fit.
In this way, they could conceive of themselves as fighting for freedom even when they were fighting to perpetuate the system of slavery.