Doesn't "one nation, indivisible" prove states can't leave?

No. "One nation, indivisible" is a line from the Pledge of Allegiance, not the Constitution, and a patriotic recitation is not law. The phrase is moving. It is also entirely beside the point, because it appears in no binding legal document and creates no legal obligation.

Where the words actually come from

The Pledge of Allegiance was written in 1892 by Francis Bellamy, a magazine writer, for a children's celebration marking the 400th anniversary of Columbus reaching the New World. It is not in the Constitution. It is not a statute. It was a composition for a school program. The phrase "under God" was not even part of it at the start. Congress added that in 1954. A line that Congress was freely editing in the middle of the twentieth century is not a binding rule about whether a state can govern itself. It is a pledge schoolchildren recite, and it carries exactly the legal weight of one.

Slogans do not create law, and the Supreme Court has said so

Set aside the Pledge for a moment, because supporters of forced union try the same move with the Constitution's own language, pointing to "a more perfect Union" in the Preamble. That argument fails for a reason the Supreme Court spelled out. In Jacobson v. Massachusetts (1905), the Court held that the Preamble "has never been regarded as the source of any substantive power conferred on the Government of the United States or on any of its Departments." If the most formal opening line of the Constitution itself grants no power and imposes no obligation, then a line from a children's pledge certainly cannot. A stirring phrase can inspire. It cannot bind.

"A more perfect Union" describes quality, not eternity

Even taken seriously, the language does not say what people assume. "More perfect" in 1787 meant more complete, more functional, better built. It does not mean permanent. The Framers were describing a union designed better than the one under the Articles of Confederation, not a union that could never end. You cannot make "forever" more forever. And the proof is in what they deleted. The Articles called the union "perpetual" and used the word freely. The Constitution never uses it once. The men who wrote it had that exact word in front of them and chose to leave it out. In law, that deletion means something.

The actual rule is silence, and silence favors the states

When you put the slogans down and read the binding text, the Constitution simply does not address a state leaving. Article I, Section 10, the list of what states may not do, does not include it. And under the Tenth Amendment, any power not handed to Washington stays with the states and the people. A power that was never delegated cannot be invented out of a line in a pledge. The Constitution's silence is not an oversight. In a system of listed powers, silence means the power stayed home.

The bottom line

"One nation, indivisible" is a beautiful thing to say and an empty thing to cite. It is a line from an 1892 school recitation, edited by Congress as recently as 1954, found in no binding law. The right of Texans to decide their own future does not rise or fall on the wording of a pledge.