The South rebelled no more or less than the United States did. Both declared themselves independent nations and then fought wars against a foreign power. Look at how the Confederacy was treated post war, as a defeated nation. The fact that no southern leader was tried for treason alone shows that the U.S. accepted there was nothing illegal about the secession. The U.S. also allowed each state to re-enter the union, again showing they had accepted the secession as legitimate. As an independent nation, the south cannot have rebelled.
I don't disagree with that, but I think the lack of post war prosecutions had more to do with the fear of another war. Only this time it would a guerilla war that would last twice as long.
There was a lot of sympathy in the north for the southern people, believe it or not; especially after the atrocities that the Federal armies committed during the war and the starvation they caused from destroying crops and strealing food from the civilians.
At Appomattox, Grant was very careful not to do anything that would cause the Confederates to fight their way out and head for the hills. Lee had already made it clear that he had allowed himself to become enveloped at Appamattox on purpose and that he no other intention than to talk and if he didn't dig what Grant had to tell him, the fit was going to hit the shan. Lee also made it clear, that without absolute immunity for his men, the war would go on. After the terms were worked out, the Confederate army, became the only enemy of the United States, in history, that was allowed to stack arms, furl their colors and march away in formation, as an army. Defeated armies of the period weren't allowed that honor.
When the Federal troops cheered, as Lee was leaving the surrender negotiations, Grant said, "I at once sent word, however, to have it stopped. The Confederates were now our countrymen, and we did not want to exult over their downfall."
Lee only surrendered the Army of Northern Virginia. There were still nearly 200,000 Confederate soldiers in the field, under arms. Grant knew that his treatment of Lee and the terms he presented would determine how and if the other Confederate armies surrendered.