Slavery may not have been the only reason for secession, but four Confederate states that published a declaration of causes for their secession (Georgia, Mississippi, South Carolina, and Texas) all made it clear that slavery was the issue for those states.
Georgia's declaration of secession begins:
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.
Mississippi's A Declaration of the Immediate Causes which Induce and Justify the Secession of the State of Mississippi from the Federal Union begins:
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. 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.
Unlike the first two, South Carolina's Declaration of the Immediate Causes Which Induce and Justify the Secession of South Carolina from the Federal Union starts with the issue of sovereign rights of states. However, after discussing the principle, the declaration identifies one, and only one, right of South Carolina that was trampled by the federal government, slavery:
The ends for which the Constitution was framed are declared by itself to be "to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defence, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity."
These ends it endeavored to accomplish by a Federal Government, in which each State was recognized as an equal, and had separate control over its own institutions. The right of property in slaves was recognized by giving to free persons distinct political rights, by giving them the right to represent, and burthening them with direct taxes for three-fifths of their slaves; by authorizing the importation of slaves for twenty years; and by stipulating for the rendition of fugitives from labor.
We affirm that these ends for which this Government was instituted have been defeated, and the Government itself has been made destructive of them by the action of the non-slaveholding States. Those States have assume the right of deciding upon the propriety of our domestic institutions; and have denied the rights of property established in fifteen of the States and recognized by the Constitution; they have denounced as sinful the institution of slavery; they have permitted open establishment among them of societies, whose avowed object is to disturb the peace and to eloign the property of the citizens of other States. They have encouraged and assisted thousands of our slaves to leave their homes; and those who remain, have been incited by emissaries, books and pictures to servile insurrection.
Texas's A Declaration of the Causes which Impel the State of Texas to Secede from the Federal Union lists slavery as the cause for secession:
The government of the United States, by certain joint resolutions, bearing date the 1st day of March, in the year A.D. 1845, proposed to the Republic of Texas, then *a free, sovereign and independent nation* [emphasis in the original], the annexation of the latter to the former, as one of the co-equal states thereof,
The people of Texas, by deputies in convention assembled, on the fourth day of July of the same year, assented to and accepted said proposals and formed a constitution for the proposed State, upon which on the 29th day of December in the same year, said State was formally admitted into the Confederated Union.
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 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.
We can argue today about the reasons for secession - historians disagree and many men who made statements during the Civil War made contradictory statements. However, at the time of secession, representatives of these four states took the time to write down the reason for secession. The legislative bodies of these states voted on and approved these statements as the reason for secession. Each of these declarations of secession list the reason as slavery.
Not so fast. Texas raised a cluster of issues, two of which you've pointed to by quoting the document in part.
Among those issues were the complaint about bad faith among the Northern States, and a conspiracy to abolish slavery w/o compensation as a major issue (given the value of slaves in Texas in 1860 was greater than that of all the improved real estate in the state put together, this was no trivial or theoretical complaint), as well as repeated failures of the Congress either to provide adequate frontier defense against incursions by Mexican bandits and Comanches, or to help defray the cost of the Ranger companies the State had raised on her own, to supply the deficit, in violation of the Constitution.
There were other complaints related to the apprehension of Wideawake agitation in Texas aimed at starting a slave revolt (after the pattern of John Brown's insurrection), arson, and other maladies the Texans accused Republicans of fomenting (rightly or wrongly, but they weren't getting any satisfaction from the federal government), and various other complaints.
"It was all about slavery" is a Marxist slogan. Their analysis is actually not so much based on Marxist theories about the value of labor, as it is a tactical offensive against Republican and conservative resistance to the Marxist takeover of the federal government.
The South today is the cradle of resistance to socialism, as it has been since the New Deal. The agitation of racial issues has been the Marxist counter, from the Civil Rights Movement to today's bloody-shirt "cracker" invective and pious posturing against Confederate symbols, all of which is cynically instrumental politicking aimed at splitting off moderate conservatives in "battleground" states like Ohio, from conservative candidates in the GOP, and at inducing RiNO/RNC panjandrums to attack and marginalize conservatives within the GOP. The Marxists' aim is to prosper the soft, "Me-Too" Republicans the rolling and mugging of whom has been liberals' and Progressives' stock in trade above 60 years now, at the expense of real conservatives who will defend the United States, capitalism, and American history.
To say that Southerners, whether FReepers or not, are secretly Kluxerphiles bent on reintroducing chattel slavery is a libel and a canard, and it's been retailed here on FR for years by Marxist trolls like Non-Sequitur, justshutupandtakeit, and other hard-line "conservative-busters".
Go ahead and take their line if you want to: but I'm telling you what it is, and why it was propagated here, and in popular historiography by the "Red diaper" historians whom Bill Clinton commissioned to rewrite the American history presented to the public by the National Park Service at our military parks, to introduce this Marxist, inculpatory blame-game meme.