The North and the South went to war for very different reasons. The South started the actual war and then the North chose to fight back.
The South went to war in order to be able to rule themselves. The South felt that, as a part of the United States, they were being dominated by the North. They felt that the North had interests that were inimical to those of the South and that the North was constantly trying to promote its interests over those of the South. The South seceded because Abraham was elected without any Southern support. They felt that he (regardless of what he said) would abolish slavery and would otherwise work to harm the South. After they seceded, they went to war when Lincoln tried to maintain Fort Sumter as they felt that this was an example of how the US would try to continue to repress the.
For the North, the cause of war was straightforward. They went to war because they did not want the South to secede. They felt that the South’s secession would harm the United States and make it a much weaker country. They feared what might happen if the South were to ally itself with strong European countries. All of this made them go to war in an attempt to preserve the Union.