Slavery was the main occasion or cause of the war, but not the only one. There were a host of other issues -- the money extracted from the South by means of the tariff, the tendency towards the concentration of power in the central government versus a balance of power between the states and the central government (the old Federalist versus Anti-Federalist argument), the failure of the central government to adequately protect the state of Texas against invasions of Indians and Mexican bandits.
Abolitionists had agitated for years over slavery. It was probably that that tipped the country into war. Things like John Brown's attempted slave revolution supported by abolitionists polarized the nation.
The South had contributed blood and money for the acquisition of the territories and yet Northern politicians wanted to restrict the rights of slaveholders to move into the territories in the face of the Dred Scot ruling and the treaty by which we obtained the Louisiana Territory. As the 1860 Republican platform said, "we deny the authority of congress, of a territorial legislature, or of any individuals, to give legal existence to slavery in any territory of the United States." Some law abiding bunch they were.
The Union changed from a voluntary one, where states were bound only by their assent, to one of force, where a band of stronger states imposed their will by the gun. Coercion of the states had been ruled out by the Founders, but it reared its ugly head largely because of Lincoln.
As you no doubt know, Congress didn't seem to think the war was about slavery. The North's objective for the first couple of years was preservation of the Union, not ending slavery. Here is a resolution of the US House of Representatives to that effect from July 22, 1861:
Resolved by the House of Representatives of the Congress of the United States, That the present deplorable civil war has been forced upon the country by the disunionists of the Southern States now in revolt against the constitutional Government, and in arms around the capitol; that in this national emergency, Congress, banishing all feelings of mere passion or resentment, will recollect only its duty to the whole country; that this war is not waged upon our part in any spirit of oppression, nor for any purpose of conquest or subjugation, nor purpose of overthrowing or interfering with the rights or established institutions of those States; but to defend and maintain the supremacy of the Constitution, and to preserve the Union, with all the dignity, equality, and rights of the several States, unimpaired; and that as soon as these objects are accomplished the war ought to cease.
The Senate passed a resolution with substantially the same wording on July 25, 1861.
On this we are in agreement.