Slavery. Specifically their desire to continue to keep owning people as property.
It's in almost every declaration of succession, when causes are listed.
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.
Mississippi
A Declaration of the Immediate Causes which Induce and Justify the Secession of the State of Mississippi from the Federal Union.
In the momentous step which our State has taken of dissolving its connection with the government of which we so long formed a part, it is but just that we should declare the prominent reasons which have induced our course.
Our position is thoroughly identified with the institution of slavery-- the greatest material interest of the world.
South Carolina
Declaration of the Immediate Causes Which Induce and Justify the Secession of South Carolina from the Federal Union
The people of the State of South Carolina, in Convention assembled, on the 26th day of April, A.D., 1852, declared that the frequent violations of the Constitution of the United States, by the Federal Government, and its encroachments upon the reserved rights of the States, fully justified this State in then withdrawing from the Federal Union; but in deference to the opinions and wishes of the other slaveholding States, she forbore at that time to exercise this right. Since that time, these encroachments have continued to increase, and further forbearance ceases to be a virtue.
...
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.
Texas
A Declaration of the Causes which Impel the State of Texas to Secede from the Federal Union.
...
In all the non-slave-holding States, in violation of that good faith and comity which should exist between entirely distinct nations, the people have formed themselves into a great sectional party, now strong enough in numbers to control the affairs of each of those States, based upon an unnatural feeling of hostility to these Southern States and their beneficent and patriarchal system of African slavery, proclaiming the debasing doctrine of equality of all men, irrespective of race or color-- a doctrine at war with nature, in opposition to the experience of mankind, and in violation of the plainest revelations of Divine Law.