Didn't Justice Scalia say there is no right to secede?

Justice Scalia offered that opinion in a personal letter, not in a court ruling, and an offhand opinion in private correspondence is not law. Even taken at face value, it does not say what people think it says.

It was a letter, not a decision

The quote comes from a private letter Justice Antonin Scalia wrote in 2006 to Dan Turkewitz, a screenwriter working on a political farce about Maine seceding from the Union. Turkewitz had written to the justices asking whether such a case might ever play out at the Supreme Court. Scalia, the only one who replied, wrote: "If there was any constitutional issue resolved by the Civil War, it is that there is no right to secede." That sentence, in a note about a movie script, is the entire basis of the claim. It was never briefed, never argued, never the subject of a case, and never joined by another justice. It carries exactly as much legal weight as any other piece of private correspondence, which is to say none.

A personal opinion is not a precedent

Courts are bound by holdings in actual cases, not by what a justice writes in his mail. If a stray sentence in private correspondence could settle a constitutional question, the law would be whatever any judge happened to tell a pen pal. Scalia, of all people, built his career on the principle that the text of the Constitution governs, and the text contains no prohibition on a state leaving the union.

His reasoning rests on the Civil War, which does not settle it

Look at what Scalia actually leaned on. Not a constitutional clause, because there isn't one, but "the Civil War." A war settles who prevailed by force. It does not settle a question of right, and it did not amend the Constitution to forbid independence. We take that argument apart in full in the question on the Civil War. The point here is that even the substance behind the famous quote is the same "the war settled it" assertion, and it fails for the same reasons.

Scalia himself said the courts would never decide this

Here is the part the talking point always leaves out. In the very same letter, Scalia wrote that he "cannot imagine that such a question could ever reach the Supreme Court," explaining that "the United States cannot be sued without its consent, and it has not consented to this sort of suit." Read that again. The justice everyone quotes against independence said plainly that the judiciary is not where this question gets resolved. That is our argument exactly. Whether a people may govern themselves is a political question, decided by the people through their political institutions, not by nine appointed judges. On the one point that was actually his to assess, Scalia agreed the courts stay out of it.

The bottom line

One justice's private letter is not a ruling, is not binding, and does not change the Constitution's silence on leaving the union. And in that same letter, Scalia conceded the question belongs to the political process, not the courts, which is exactly where the Texas Nationalist Movement has always said it belongs. The right of self-government does not rise or fall on a piece of fan mail.