The Confederacy? The interest seems to be the act of slavery and the war Lincoln is talking about must be the Civil War, which was taking place while Lincoln was addressing his second inaugural. Lincoln was reasoning that the Confederacy was fighting to keep slavery, which is the interest the "insurgents" have. Lincoln also did not want slavery to continue to spread, but he was fine with having slavery, "restrict the territorial enlargement if [slavery]".
Because they are separated from the rest of the world
