Well, let's look at the words of the Southerners themselves. Confederate Vice President Alexander Stephens gave a speech known as the Cornerstone Speech, in which he declared:

The prevailing ideas entertained by him [Thomas Jefferson] and most of the leading statesmen at the time of the formation of the old constitution, were that the enslavement of the African was in violation of the laws of nature; that it was wrong in principle, socially, morally, and politically [...] Those ideas, however, were fundamentally wrong. They rested upon the assumption of the equality of races. This was an error. 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. [emphasis added]

The state of Mississippi also issued "A Declaration of the Immediate Causes which Induce and Justify the Secession of the State of Mississippi from the Federal Union" in which they declared:

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.

Texas was no less direct in their devotion to the Peculiar Institution:

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 [...] We hold as undeniable truths that the governments of the various States, and of the confederacy itself, were established exclusively by the white race, for themselves and their posterity; that the African race had no agency in their establishment; that they were rightfully held and regarded as an inferior and dependent race, and in that condition only could their existence in this country be rendered beneficial or tolerable. That in this free government all white men are and of right ought to be entitled to equal civil and political rights; that the servitude of the African race, as existing in these States, is mutually beneficial to both bond and free, and is abundantly authorized and justified by the experience of mankind, and the revealed will of the Almighty Creator" [emphasis added]

Careful reading of these documents shows that the "rights" the Southerners complain about being denied are exclusively the rights of slave-holders, like Northern states denying rights of transit or defying the Fugitive Slave Act in deference to their own state laws (which contradicts neo-Confederate claims that the war was fought over state's rights). These documents, and the ensuing century and a half of legalized segregation and Jim Crow laws would seem to demonstrate that most Southerners didn't necessarily believe that African Americans didn't deserve rights, but that they had already given African Americans all the rights they did deserve.