It's slavery through and through. States rights simply formed the then-convenient rhetorical justification for secession and for various anti-majoritarian positions adopted with the aim of safeguarding slavery in an increasingly hostile (or at least apparently hostile) Union. If they genuinely believed in what they preached, then proslavery Southerners would have created a radically different antebellum era.

The most damning testimony to this fact is right there in the Declarations of the Causes of Secession passed by four of the seceding states. This is from South Carolina's:

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. The States of Maine, New Hampshire, Vermont, Massachusetts, Connecticut, Rhode Island, New York, Pennsylvania, Illinois, Indiana, Michigan, Wisconsin and Iowa, have enacted laws which either nullify the Acts of Congress or render useless any attempt to execute them. In many of these States the fugitive is discharged from service or labor claimed, and in none of them has the State Government complied with the stipulation made in the Constitution. The State of New Jersey, at an early day, passed a law in conformity with her constitutional obligation; but the current of anti-slavery feeling has led her more recently to enact laws which render inoperative the remedies provided by her own law and by the laws of Congress. In the State of New York even the right of transit for a slave has been denied by her tribunals; and the States of Ohio and Iowa have refused to surrender to justice fugitives charged with murder, and with inciting servile insurrection in the State of Virginia. Thus the constituted compact has been deliberately broken and disregarded by the non-slaveholding States, and the consequence follows that South Carolina is released from her obligation.

Notice that an act by a state that nullified federal law was seen as just grievance for Carolina to quit the Union. Had they possessed a genuine enthusiasm for states rights qua states rights, they'd have been applauding that kind of thing.

Here's Mississippi:

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.

Georgia:

For the last ten years we have had numerous and serious causes of complaint against our non-slave-holding confederate States with reference to the subject of African slavery.

And Texas:

She was received as a commonwealth holding, maintaining and protecting the institution known as negro slavery-- the servitude of the African to the white race within her limits-- a relation that had existed from the first settlement of her wilderness by the white race, and which her people intended should exist in all future time. Her institutions and geographical position established the strongest ties between her and other slave-holding States of the confederacy. Those ties have been strengthened by association. But what has been the course of the government of the United States, and of the people and authorities of the non-slave-holding States, since our connection with them?

The controlling majority of the Federal Government, under various pretences and disguises, has so administered the same as to exclude the citizens of the Southern States, unless under odious and unconstitutional restrictions, from all the immense territory owned in common by all the States on the Pacific Ocean, for the avowed purpose of acquiring sufficient power in the common government to use it as a means of destroying the institutions of Texas and her sister slaveholding States.

And here's the Provisional Vice-President of the Confederacy, Alexander Stephens of Georgia:

Our new Government is founded upon exactly the opposite ideas; its foundations are laid, its cornerstone rests, upon the great truth that the negro is not equal to the white man; that slavery, subordination to the superior race, is his natural and moral condition. [Applause.] This, our new Government, is the first, in the history of the world, based upon this great physical, philosophical, and moral truth.

I've written also a few previous answers that delve into the subject in detail which you might find helpful. The last link specifically examines just what proslavery Southerners really did when they had a free hand and so best expressed their genuine constitutional scruples. Questions and comment are, of course, welcome. I just don't want to retype it all at the moment. :)

One can't engage in a discussion about the genus of the US Civil War without talking about BOTH state's rights and slavery: the two issues were interconnected and codependent. More on that in a moment; for now, consider this 20th century comparison: was the rise of Nazi Germany the result of harsh conditions imposed on that country following the Treaty of Versailles, or the product of one man's (Hitler's) ability to exploit the long-standing racial biases, not to mention the political and economic weaknesses, of the continent following WWI? Most would agree that the answer is a combination of all of that, and that it would have been difficult to foster one without the other. Indeed, WWII was the end result of more than a hundred years of unresolved political and cultural disputes within Europe that spread like a virus throughout much of the world. Likewise, the US Civil War was the result of a number of poorly-conceived compromises that kicked important issues like slavery and state's rights down the road for another generation to deal with. Consider the fact that Hamilton, Jefferson, and Washington were already arguing over the scope and ruling authority of the US government in the 1790s when the issue of a national bank came up. So you can see that pretty much as soon as the US declared independence, there was already a heated argument among the top guys about how much power the government would have over the individual states. On one side, you had people like Hamilton, who believed in a strong central government in the model of European nations of the time (minus the monarchy, of course), while on the other, you had Jefferson expounding the virtues of small-government and minimal federal interference. A series of compromises followed from this, most famously the Missouri Compromise of 1820. Although this was nominally about the expansion of slavery into new territories, its roots were laid in the question of state-vs-federal rights that had so divided the "Founding Fathers." When the Civil War began to break out at the end of 1860 (and then began as an actual conflict in 1861), you have to remember that it wasn't because Lincoln had made a proclamation to free the slaves. Quite the opposite: Lincoln was aware of Southern discontent and their fear of forced emancipation, and he promised that he would do no such thing (again, this was in late-1860...things changed after secession, of course). The reason the Southern states broke off in 1860/61 was as a result of their expectation that Lincoln represented a strong Federal presence in the White House, and that he would use that Executive power to enact policies and laws that ran counter to the cultural climate south of the Mason Dixon. There was a definite perception that Lincoln was pro-abolition, and this certainly contributed to the secession sentiment, yet at the time (and primary sources of the day back this up) the states that broke off from the Union, and their representatives, claimed that they were doing it to protect their rights as autonomous states under no obligation to follow federal law they disagreed with. Of course, after the Emancipation Proclamation, Lincoln crafted the terms of the war to reflect a higher moral struggle (against slavery), and the question about slavery and its expansion was undeniably the igniting spark of the conflict, yet to say that the conflict was the result of slavery and not state's rights is reductive and simply not true. [Sources: Bruce Catton, 'Mr. Lincoln's Army'; Douglas Southall Freeman, 'Lee's Lieutenants, vol. 1'; Shelby Foote, 'The Civil War, A Narrative, vol. 1']

fyi, you'll find more on this in the FAQ

• The Civil War and Slavery