Texas as an example
Q: Doesn't the Texas Constitution reserve the right of Texas to secede?
This heavily popularized bit of Texas folklore finds no corroboration where it counts: No such provision is found in the current Texas Constitution (adopted in 1876) or the terms of annexation. However, it does state (in Article 1, Section 1) that "Texas is a free and independent State, subject only to the Constitution of the United States..." (note that it does not state "...subject to the President of the United States..." or "...subject to the Congress of the United States... " or " ...subject to the collective will of one or more of the other States..." )
Neither the Texas Constitution, nor the Constitution of the united States, explicitly or implicitly disallows the secession of Texas (or any other "free and independent State" ) from the United States. Joining the "Union" was ever and always voluntary, rendering voluntary withdrawal an equally lawful and viable option (regardless of what any self-appointed academic, media, or government "experts"—including Abraham Lincoln himself—may have ever said).
Both the original (1836) and the current (1876) Texas Constitutions also state that "All political power is inherent in the people ... they have at all times the inalienable right to alter their government in such manner as they might think proper."
Likewise, each of the united States is "united" with the others explicitly on the principle that "governments derive their just powers from the consent of the governed" and "whenever any form of government becomes destructive to these ends [i.e., protecting life, liberty, and property], it is the right of the people to alter or to abolish it, and to institute new government" and "when a long train of abuses and usurpations...evinces a design to reduce them under absolute despotism, it is their right, it is their duty, to throw off such government, and to provide new guards for their future security."
Q: Didn’t the outcome of the “Civil War” prove that secession is not an option for any State?
No. It only proved that, when allowed to act outside his lawfully limited authority, a U.S. president is capable of unleashing horrendous violence against the lives, liberty, and property of those whom he pretends to serve. The Confederate States (including Texas) withdrew from the Union lawfully, civilly, and peacefully, after enduring several decades of excessive and inequitable federal tariffs (taxes) heavily prejudiced against Southern commerce. Refusing to recognize the Confederate secession, Lincoln called it a "rebellion" and a "threat" to "the government" (without ever explaining exactly how "the government" was "threatened" by a lawful, civil, and peaceful secession) and acted outside the lawfully defined scope of either the office of president or the U.S. government in general, to coerce the South back into subjugation to Northern control.
The South's rejoining the Union at the point of a bayonet in the late 1860s didn't prove secession is "not an option" or unlawful. It only affirmed that violent coercion can be used—even by governments (if unrestrained)—to rob men of their very lives, liberty, and property.
It bears repeating that the united States are "united" explicitly on the principle that "governments derive their just powers from the consent of the governed" and "whenever any form of government becomes destructive to these ends [i.e., protecting life, liberty, and property], it is the right of the people to alter or to abolish it, and to institute new government" and "when a long train of abuses and usurpations...evinces a design to reduce them under absolute despotism, it is their right, it is their duty, to throw off such government, and to provide new guards for their future security."
Q: Didn’t the U.S. Supreme Court decision in Texas v. White prove that secession is unconstitutional?
No. For space considerations, here are the relevant portions of the Supreme Court's decision in Texas v. White:
"When Texas became one of the United States, she entered into an indissoluble relation. The union between Texas and the other States was as complete, as perpetual, and as indissoluble as the union between the original States. There was no place for reconsideration or revocation, except through revolution or through consent of the States.
"...The obligations of the State, as a member of the Union ...remained perfect and unimpaired. ...the State did not cease to be a State, nor her citizens to be citizens of the Union.
"...Our conclusion therefore is, that Texas continued to be a State, and a State of the Union."
— Texas v. White, 74 U.S. 700, 703 (1868)
It is noteworthy that two years after that decision, President Grant signed an act entitling Texas to U.S. Congressional representation, readmitting Texas to the Union.
What's wrong with this picture? Either the Supreme Court was wrong in claiming Texas never actually left the Union (they were — see below), or the Executive (President Grant) was wrong in "readmitting" a state that, according to the Supreme Court, had never left. Both can't be logically or legally true.
To be clear: Within a two year period, two branches of the same government took action with regard to Texas on the basis of two mutually exclusive positions — one, a judicially contrived "interpretation" of the US Constitution, argued essentially from silence, and the other a practical attempt to remedy the historical fact that Texas had indeed left the Union, the very evidence for which was that Texas had recently met the demands imposed by the same federal government as prerequisite conditions for readmission. If the Supreme Court was right, then the very notion of prerequisites for readmission would have been moot — a state cannot logically be readmitted if it never left in the first place.
This gross logical and legal inconsistency remains unanswered and unresolved to this day.
Now to the Supreme Court decision in itself...
The Court, led by Chief Justice Salmon Chase (a Lincoln cabinet member and leading Union figure during the war against the South) pretended to be analyzing the case through the lens of the Constitution, yet not a single element of their logic or line of reasoning came directly from the Constitution — precisely because the Constitution is wholly silent on whether the voluntary association of a plurality of states into a union may be altered by the similarly voluntary withdrawal of one or more states.
It's no secret that more than once there had been previous rumblings about secession among many U.S. states (and not just in the South), long before the South seceded. These rumblings met with no preemptive quashing of the notion from a "constitutional" argument, precisely because there was (and is) no constitutional basis for either allowing or prohibiting secession.
An objective reading of the relevant portions of the White decision reveals that it is largely arbitrary, contrived, and crafted to suit the agenda which it served: presumably (but unconstitutionally) to award to the U.S. federal government, under color of law, sovereignty over the states, essentially nullifying their right to self-determination and self-rule, as recognized in the Declaration of Independence, as well as the current Texas Constitution (which stands unchallenged by the federal government).
Where the Constitution does speak to the issue of powers, they resolve in favor of the states unless expressly granted to the federal government or denied to the states. No power to prevent or reverse secession is granted to the federal government, and the power to secede is not specifically denied to the states; therefore that power is retained by the states, as guaranteed by the 10th Amendment.
The Texas v. White case is often trotted out to silence secessionist sentiment, but on close and contextual examination, it actually exposes the unconstitutional, despotic, and tyrannical agenda that presumes to award the federal government, under color of law, sovereignty over the people and the states.