The South was also fighting for slavery. Read what the states themselves said about why they were leaving the Union.
Georgia:
” The people of Georgia, after an equally full and fair and deliberate hearing of the case, have declared with equal firmness that they shall not rule over them. A brief history of the rise, progress, and policy of anti-slavery and the political organization into whose hands the administration of the Federal Government has been committed will fully justify the pronounced verdict of the people of Georgia. The party of Lincoln, called the Republican party, under its present name and organization, is of recent origin. It is admitted to be an anti-slavery party.”
Mississippi:
“In the momentous step which our State has taken of dissolving its connection with the government of which we so long formed a part, it is but just that we should declare the prominent reasons which have induced our course.
Our position is thoroughly identified with the institution of slavery— the greatest material interest of the world. Its labor supplies the product which constitutes by far the largest and most important portions of commerce of the earth. These products are peculiar to the climate verging on the tropical regions, and by an imperious law of nature, none but the black race can bear exposure to the tropical sun.”
South Carolina:
“The General Government, as the common agent, passed laws to carry into effect these stipulations of the States. For many years these laws were executed. But an increasing hostility on the part of the non-slaveholding States to the institution of slavery, has led to a disregard of their obligations, and the laws of the General Government have ceased to effect the objects of the Constitution.”
http://www.civilwar.org/education/history/primarysources/declarationofcauses.html
In fact, Lincoln offered, as a peace gesture, not to interfere with slavery where it existed and promised to enforce the Fugitive Slave Law in the North, as long as the Federal government could collect tariffs in Southern ports. For the first year and a half of the war, emancipation was not a war strategy of the Lincoln Administration.
Tariffs, as well as slavery, were primary issues that led to the Southern secession. After all, why would the large majority of Confederate soldiers come from non-slaveholding homes? Concern on the effects of high tariffs to their livelihoods, as well as patriotism to their native states, motivated Johnny Reb for the most part.