Saying "slavery" is simplistic if that is all he says. Of course like any historical event (and event) there are many different factors and causes. There is an extensive post hoc effort to say that slavery was not the issue, that it was states' rights or tariffs or something. But "slavery" is the best one word answer, we can see that by looking at what the seceding states themselves said:

South Carolina Declaration of Independence

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. 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.

Georgia:

The people of Georgia having dissolved their political connection with the Government of the United States of America, present to their confederates and the world the causes which have led to the separation. 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. They have endeavored to weaken our security, to disturb our domestic peace and tranquility, and persistently refused to comply with their express constitutional obligations to us in reference to that property, and by the use of their power in the Federal Government have striven to deprive us of an equal enjoyment of the common Territories of the Republic. This hostile policy of our confederates has been pursued with every circumstance of aggravation which could arouse the passions and excite the hatred of our people, and has placed the two sections of the Union for many years past in the condition of virtual civil war. Our people, still attached to the Union from habit and national traditions, and averse to change, hoped that time, reason, and argument would bring, if not redress, at least exemption from further insults, injuries, and dangers. Recent events have fully dissipated all such hopes and demonstrated the necessity of separation.

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. 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. These products have become necessities of the world, and a blow at slavery is a blow at commerce and civilization. That blow has been long aimed at the institution, and was at the point of reaching its consummation. There was no choice left us but submission to the mandates of abolition, or a dissolution of the Union, whose principles had been subverted to work out our ruin. That we do not overstate the dangers to our institution, a reference to a few facts will sufficiently prove.

Texas:

Texas abandoned her separate national existence and consented to become one of the Confederated Union to promote her welfare, insure domestic tranquility and secure more substantially the blessings of peace and liberty to her people. She was received into the confederacy with her own constitution, under the guarantee of the federal constitution and the compact of annexation, that she should enjoy these blessings. 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?

FYI, there are a bunch of posts in the FAQ that tackle this question in depth

• The American Civil War | Causes

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While it may seem crazy to you, it is absolutely true. Slavery had been the dominant force in American politics for the entire decade of the 1850s, and in a sense a little bit longer. The Compromise of 1850 forced Northerners who had been trying to avoid thinking about slavery to grapple with the issue. Enforcement of the fugitive slave act meant that Northern law enforcement and judicial systems were mandated to help with the apprehension and return of fugitive slaves. High profile cases where fugitives were apprehended in the North put a local, human face on slavery. The novel Uncle Tom's Cabin--a bestseller unlike any other book in American history to this point--created a sympathetic and moderate model for antislavery identity (prior to this point abolitionists were easily marginalized as wild-eyed radicals for the most part). The rise of free soil politics, which argued that slavery was a threat to ordinary white workers and that saw the expansion of slave territory as a manifest danger worth fighting over provided another outlet for northern antislavery which due to its anti-black overtones could appeal to an even more conservative segment of the Northern population than Stowe or radicals like Garrison.

At the same time, slavery became even more entrenched in the South. Cotton prices rose, new plantations came online, and the increasing ubiquity of slave powered industry gave ordinary, non-slaveholding Southerners a stake in the slave system and allowed middle-class Southerners to envision slavery as a force that could modernize the South. At the same time, the southern states banned abolitionist periodicals and voicing discontent with slavery was a perilous opinion to espouse in the South, where vigilante justice was not uncommon and where murder rates were 4 times that of the antebellum North. Increasingly there were a series of flashpoints that polarized the two sides; Bleeding Kansas, John Brown's Raid, and the caning of Sumner all occurred over the course of the late 1850s and all were motivated by clashes of ideals over slavery. By the time Lincoln had been elected president, it was impossible for entrenched Southern interests to submit to a chief executive who opposed slavery's expansion and who could envision its end. And then we had a civil war.