"Flying, say, Bismark's flag, the rising sun battle flag, or Saddam's Iraqi standard would be just as offensive, and, I would guess, not readily defended by many who defend flying the Confederate flag."
Important to note that the CSA was former states of the United States who VOTED to secede from the US, which made no specific provision allowing OR disallowing secession.
Rebellion implies an effort to overthrow washington, which simply wasn't the case. The seceding states said 'we are leaving.' Not 'we are taking over YOUR fedgov,' which is rebellion.
You need to realize the secession question wasn't just invented in 1860; it had been raised continuously in the 19th century and avoided by politicians who were able to work out arrangements to avoid it. Congress never clarified its legality to my knowledge, despite decades of having the issue raised, particularly with the status of new states being added to the union. Given the much greater prominence the states had with the identities of the citizens in how they identified themselves, I cannot imagine that it was widely believed that secession was illegal.
This seems somewhat different than the various flags of foreign powers the US has fought (and usually defeated).
If I remember correctly, the New England states considered seceeding during Jefferson's Presidency, didn't they?
No, rebellion is defined as "open, armed, and usually unsuccessful defiance of or resistance to an established government." A reasonable description of the southern actions.