It's nice to think that somehow the CSA or the antebellum US were just a bunch of anti-government guys who only wanted to do as they pleased before bad old Abe came along and made everything dictatorial, but they were governments (or aspired to be governments) and some who came under their own power had as many legitimate grievances as subjects ever do.
The bigger issue is being deprived of a vote in the Congress; see the linked articles [in the previous post] on the events surrounding the 14th Amendment, which is supported by congressional records.