I would say the primary reason was "the Federal Government, and its encroachments upon the reserved rights of the States."
South Carolina, and other agricultural states, had been fighting a tariff war against the industrial states for decades; but by 1860 the North had grown in size, and had enough power to plunder the South with a protectionist tariff, if not before the election, then afterward; and they wasted no time in presenting it for a vote. It passed overwhelmingly in the House, but was delayed in the Democrat-controlled Senate. By the time it came up for vote in the Senate, several Southern states had already seceded and the Republicans were in control.
Unequal taxation was heavily emphasized in the S.C. Convention:
"And so with the Southern States, towards the Northern States, in the vital matter of taxation. They are in a minority in Congress. Their representation in Congress, is useless to protect them against unjust taxation; and they are taxed by the people of the North for their benefit, exactly as the people of Great Britain taxed our ancestors in the British parliament for their benefit. For the last forty years, the taxes laid by the Congress of the United States have been laid with a view of sub-serving the interests of the North. The people of the South have been taxed by duties on imports, not for revenue, but for an object inconsistent with revenue— to promote, by prohibitions, Northern interests in the productions of their mines and manufactures.
"There is another evil, in the condition of the Southern towards the Northern States, which our ancestors refused to bear towards Great Britain. Our ancestors not only taxed themselves, but all the taxes collected from them, were expended amongst them. Had they submitted to the pretensions of the British Government, the taxes collected from them, would have been expended in other parts of the British Empire. They were fully aware of the effect of such a policy in impoverishing the people from whom taxes are collected, and in enriching those who receive the benefit of their expenditure. To prevent the evils of such a policy, was one of the motives which drove them on to Revolution. Yet this British policy, has been fully realized towards the Southern States, by the Northern States."
["The Address of the People of South Carolina Assembled in Convention, to the People of the Slaveholding States of the United States." Evans & Cogswell, Dec 25, 1860, pp.6-7]
For most of my long life I too believed the war was fought over slavery.
Mr. Kalamata
The United States went to war because it's fort was fired upon by rebel forces that had gained control of the state of south Carolina. The United States fought to suppress a rebellion. They later added the war aim of freeing the slaves.
Here's a breakdown of the context of Georgia, Mississippi, South Carolina, and Texas's ordinances of secession. Keep in mind that when the phrase states rights is used it's almost exclusively to the right to travel freely with slaves, expansion of slavery into the western territories, holding slaves, etc.
Georgia: 56% Slavery; 23% Economic issues; 15% Context; 4% States' Rights; 2% Lincoln's Election
Mississippi: 73% Slavery; 20% Context; 3% States' Rights; 4% Contest
South Carolina: 37% States' Rights 41% Context; 20% Slavery; 2% Lincoln's election
Texas; 54% Slavery; 21% States' Rights; 15% Context; 6% Military Protection; 4% Lincoln's Election
You can look at the documents yourself and verify what I have posted.