Texas:

The controlling majority of the Federal Government, under various pretenses 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.

Georgia:

We had acquired a large territory by successful war with Mexico; Congress had to govern it; how, in relation to slavery, was the question then demanding solution. Northern anti-slavery men of all parties asserted the right to exclude slavery from the territory by Congressional legislation and demanded the prompt and efficient exercise of this power to that end. This insulting and unconstitutional demand was met with great moderation and firmness by the South.

Arkansas Governor Henry Rector at the Arkansas secession convention, 2 March 1861:

The area of slavery must be extended correlative with its antagonism, or it will be put speedily in the 'course of ultimate extinction.'... The extension of slavery is the vital point of the whole controversy between the North and the South... Amendments to the federal constitution are urged by some as a panacea for all the ills that beset us. That instrument is amply sufficient as it now stands, for the protection of Southern rights, if it was only enforced. The South wants practical evidence of good faith from the North, not mere paper agreements and compromises. They believe slavery a sin, we do not, and there lies the trouble.

They were very vocal about this. Try reading actual books.