The fear that the rise of the Republican Party, a party founded on anti slavery credentials, was going to end, or at least seriously interfere with, their "peculiar institution". Whether right or wrong - Lincoln himself had, at least publicly, made no proclamation that he intended anything other than hopefully to prevent its further expansion (although that was enough to scare them too), and that he did not wish to remove it from the states where it was already legal - the South certainly believed it to be quite possible he intended the ultimate. Additionally,they felt more directly threatened by the Northern States who often were refusing to enforce the fugitive Slave Act (Which some might call an ironic complaint, given how they liked to holler about states' rights.)
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.
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?
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 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.
As you can see, slavery was intimately tied to their cause of secession. That isn't to say that it alone was the reason, but much of the other reasons often tied back into slavery anyways. If you look at the Nullification Crisis for instance, the tariffs on imported good were obviously seen as beneficial to the Industrial North, at the expense of the Agrarian South. Although not directly an assault on slavery, many of the pro-nullification supporters, principally Calhoun, certainly thought it was a backdoor attempt to interfere, by making the south more and more dependent on the Northern manufacturers and bankrupting the Southern slaveholders. (Whether that was the intent of the North, someone else would have to weigh in on. I would merely point out that it was the Southerners who explicitly tied the issue to slavery).
So anyways, the primary motivation was to protect the institution of slavery. Simple as that.