From Dean Obeidallah on the reason for secession.

This history alone should dissuade anyone from ever displaying the Confederate battle flag on U.S. soil again. But for those still on the fence, these words from the vice president of the Confederacy, Alexander Stephens, explaining the genesis of the Confederacy should end any doubts -- as well as make your blood boil.

In 1861, Stephens explained to a cheering audience that the Confederacy was founded to expressly reject the proposition that men of all races were equal. Instead, Stephens stated, "The foundations of our new government 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.

https://www.cnn.com/2013/10/25/opinion/obeidallah-confederate-flag/index.html

The full speech 

https://sourcebooks.fordham.edu/mod/1861stephens.asp

Edit to add:

On secession itself 

Texas v. White

Supreme Court of the United States

Argued February 5, 1869
Decided April 12, 1869Full case nameTexas v. White, et al.Citations74 U.S. 700 (more)

7 Wall. 700; 19 L. Ed.227; 1868 U.S. LEXIS1056; 1868 WL 11083

HoldingTexas (and the rest of the Confederacy) never left the Union during the Civil War, because a state cannot unilaterally secede from the United States. 
Treasury bond sales by Texas during the war were invalid, and the bonds were therefore still owned by the post-war state.Court membership

Chief Justice

Salmon P. Chase

Associate Justices

Samuel Nelson ·  Robert C. Grier
Nathan Clifford ·  Noah H. Swayne
Samuel F. Miller ·  David Davis
Stephen J. Field

Case opinionsMajorityChase, joined by NelsonConcurrenceClifford, Davis, FieldConcur/dissentSwayne, joined by MillerDissentGrierLaws appliedU.S. Const. art. IV

Texas v. White, 74 U.S. (7 Wall.) 700 (1869), was a case argued before the United States Supreme Court in 1869.[1] The case involved a claim by the Reconstruction government of Texas that United States bonds owned by Texas since 1850 had been illegally sold by the Confederate state legislature during the American Civil War. The state filed suit directly with the United States Supreme Court, which, under the United States Constitution, retains original jurisdiction on certain cases in which a state is a party.

In accepting original jurisdiction, the court ruled that, legally speaking, Texas had remained a United States state ever since it first joined the Union, despite its joining the Confederate States of America and its being under military rule at the time of the decision in the case. In deciding the merits of the bond issue, the court further held that the Constitution did not permit states to unilaterally secede from the United States, and that the ordinances of secession, and all the acts of the legislatures within seceding states intended to give effect to such ordinances, were "absolutely null".[2

https://en.wikipedia.org/wiki/Texas_v._White