I believe the "Civil War was about states' rights" line began in the 19th century [1], around the same time as "the number of Confederate memorial installations peaking around 1910 — 50 years after the end of the Civil War and at the height of Jim Crow" [2].
In reality, "Confederate states did claim the right to secede, but no state claimed to be seceding for that right. In fact, Confederates opposed states’ rights — that is, the right of Northern states not to support slavery" in "Northern states [failing] to 'fulfill their constitutional obligations' by interfering with the return of fugitive slaves to bondage" [3].
Unless you have a very subtle point that I'm missing, I think you got tripped up with the numbering of the centuries. The "19th century" started in 1801 and ended in 1900 (https://en.wikipedia.org/wiki/19th_century) putting the Civil War itself in the late-middle of the 19th century.