The case turns on the meaning of Section 3 of the 14th Amendment, ratified after the Civil War, which bars those who had taken an oath “to support the Constitution of the United States” from holding office if they then “shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof.”
Imagine you can be kept off the ballot for being five signatures short of a full page, but doing an insurrection isn’t a good reason. And the individual states can decide on the first thing but not the second. Wild.