If you are admitting that the Confederacy was the belligerent then why do you refer to it as "Lincoln's optional war"? Is your complaint that Lincoln didn't immediately surrender when the Confederacy started it?
“If you are admitting that the Confederacy was the belligerent . . .”
The South was a belligerent. The North was a belligerent. Both were belligerents. The recognition of a nation as a belligerent in a war does not imply their cause is right or wrong.