Actually, every educated person at the time of the Civil War understood that the Declaration of Independence and the Constitution supported secession. Since a union is built on voluntary cooperation for the pursuit of common goals, a member can also leave (secede) from the group if its needs are not being met, if it feels manipulated, if terms of the contract have been broken by the other party, or if the contract no longer serves the needs of the seceding member.
Texas declared the right to secede from Mexico because the contract between them had been broken by Mexico. Independence was declared on March 2, 1836. People in the United States approved. Texas must have felt confused when seceding from the United States during the Civil War for the same reason was harshly denounced!
Oh, well, but that was seceding from Mexico. Did anyone secede from the United States before the Civil War? No, but some New England states threatened to secede in 1803 and 1814.
And then there was secession within a state. During the Civil War, New York City seriously considered seceding from the United States to establish a separate State from New York. It would then declare neutrality and trade with both the USA and CSA!
Also, the United States didn’t object to West Virginia seceding from Virginia during the Civil War because that was to the advantage of the U.S.A. In fact, it was planned by the Lincoln administration.
When I was a child, we said the Pledge of Allegiance daily. Remember the word “indivisible?” Have you ever thought about that?