That quote you mention is from the Declaration of Independence and is not a legally binding document of any kind. It has no more relevance to the real governance of this nation than does the oft-cited quotation from the same document regarding "our creator." What that document refers to and the section quote is revolution. The founding fathers knew full well that they had no legal right to secede and war was inevitable because of their declaration. Secession is the peaceful breaking off from another state in a legal manner.
No legal, but a strong moral right to secede. I know full well that the DOI has no legal standing, however it does lay out a very strong moral argument as to when secession is to be expected and undertaken (notice, I didn't say "allowed").
There have been several rulings since the CW that have said states do not have the right to secede. The 10th amendment has been construed by those unhappy with the federal government to mean that if they don't like what's going on at a federal level, they can just go about their merry way but the courts have said otherwise. In other words, the states themselves are part of the United States of America, not "free agent" countries that happen to be loosely connected to the US, picking and choosing which laws they will follow and what they will contribute to the union and choosing to leave when it becomes convenient to do so (the Constitution cleared this up from the much looser Articles of Confederation). Now, if a state would like to commit to revolution, they may elect to do so but they would be in open rebellion/sedition (as much as the founders of this nation were to England) and would be put down very quickly.
So all court rulings are correct? Jim Crow was right? I think not.
Besides, what do you expect a Federal court to rule? That the CW was fought for specious reasons? Pshaw!

(Hrm...this CT stuff is kinda fun...)
If you don't see the Union as sacred, why would you see the state as sacred? First, you talk about the right to secede being inherent in the people, calling them sovereign. Later, you claim that it's the states that have that right.
The People are the Soverign in the US. The States, and the Federal Government for that matter, draw their authority from the People. That is the very foundation upon which the US is founded. That it doesn't play out that way as a practical matter is a discussion for another day. My point is that if a majority of the People agree that State X gets to secede, the it should secede. If Texas, say, felt so strongly that it's needs were not being met by being pat of the Union, then they should be allowed to secede. This doesn't mean that it's neighbors have to engage in trade with them, mind you, or follow any of the reciprical laws (marriage etc) that are afforded them as part of the Union.
What if a unit of people smaller than the state wanted to secede? What if everybody in Marin County, California voted to secede from the Union? Do you believe they should be able to? If not, explain how the cohesiveness of a county creates less sovereignty than that of a state.
Never thought about it, but I'd probably come down on letting them make a go for it. They'll be back soon enough once the utility rates go through the roof due to tariffs with the State of California, grocery bills do the same etc etc.
What if the people in a state are not unanimous and cannot be separated by geography? If 73% of Texas voters want to secede, why should their political will be more important than Texans who don't? Should the minority be marched to Oklahoma and thrown out or made subservient to the will of the majority of voters? By what right are the majority acting in throwing out or ignoring the minority?
Hrm....another from hypothectical land. Ok, we can play the "what if" game for a while. It won't change the fact that there's nothing explict in any governing document that forbids a state from seceding.
Well, once Texas (in this example) secedes, then those that are unhappy would probably migrate to the neighboring states. OK, LA, NM and Mexico would all problably see a bump in population. Those who stayed would propbaly work to get it back in the Union. As for if it's right? That's for one who's more of a philosopher than I, but it's allowed by our system. Was it right for the founding fathers to rebel against Great Britian? Probably not from a legal sense....
Again, stop thinking that this is done over trivial matters. To get that many people to agree on the disolution of political ties with the rest of the US enough that they'd actually act (as opposed to just pissing and moaning about it) would take a situation much like we saw leading up to 1776.
Similarly, what if 51% of Texans want to secede but 93% of all Americans don't want them to? Why should the happenstance of state borders dictate the size of the unit that that gets to decide on secession? If most Americans don't want Texas out, why should we ignore their political will only to focus on the will of the people who happen to have been born slightly north of Mexico?
Well, then the 93% can petition their representatives to not trade with the new Republic of Texas.
Why should a "state" even be a political entity? There's nothing inherent in the concept of popular sovereignty to even suggest such a thing.
Yeah...ok...for that matter why should a "nation" even be a political entity? There's nothing inherent in the concept of popular sovereignty to even suggest such a thing. At what level do you want to deal with this? We can play this game all over the place. All political bounaries are well established fictions. Go to the boarder of New York and Pennslyvania and other than the street signs, there are no real indications that there's any difference, is there? It's a collective agreement made hundreds of years ago. If we, today, do not agree with those reasonings, cannot e change them?
Now, having said all that. I don't think this would ever, in a million years
1, happen, for some of the reasons that I alluded to before. If things were so contentious that Texas left, how much to you think that the rest of US would want to deal with them? Probably very little, especially at first. So, if Mexico didn't make them a good offer, they'd probably come back and petition for statehood.
Oh, and one final thing. If statehood is such a great thing, why has Guam and Porto Rico turned it down? Why don't the Feds just march in there and force them to join the Union like Lincoln did to the Confederacy? Granted, they're territiories which makes their status a little different, but if we're saying that you can't be part of the US without being a State, why not Guam and PR?
1 "in a million years" in the coloquial sense. A lot of things can happen in a literal million years.