"Likewise, the sovereign had a lawful right, some would add obligation, to suppress rebellion,"

Defination of Rebellion:

"A rebellion is, in the most general sense, a refusal to accept authority. It may therefore be seen as encompassing a range of behaviours from civil disobedience to a violent organized attempt to destroy established authority. It is often used in reference to armed resistance against an established government, but can also refer to mass nonviolent resistance movements. Those who participate in rebellions are known as "rebels"."

Cleanly both the American Revolution and the Ameriacn Civil War were rebellions in the sence that they were attempts to dissolve their bonds with their previous governmental body.

But were either of them a violent attempt to "Destroy the established Authority" of either the King, of England or the Federal Government in Washington DC?

Had either the American Colonies or the Southern states been allowed to leave peaceable, would King George not have still been the King of the remaining English Empire and Lincoln the President of the remaining United States?

If the southern act of secession was rebellion, then the Civil rights movement of the 50's and 60's was rebellion also against the lawful authority of the States.

You can not have one defination one time and another defination at another time.