"The overwhelming majority of southerners ... fought because Lincoln's army was on their doorsteps shooting at them, and when you get shot the obvious thing to do is shoot back!"
The overwhelming majority of southerners, even excluding free and enslaved blacks, did not fight at all.
To the extent that those in the south who did take up arms, largely took them up in the southern cause, is accepted fact.
I would add to the list the border slave state of Maryland (and possibly Delaware too), which provided a large number of troops to both sides. And, though there are some who would deny it, a substantial number of aboriginal Americans fought "for the Union" (recognizing that inter-tribal rivalries may have been a more significant factor in their alliances).
Post your stats and sources then. We already know that a higher percentage of the southern population fought in the armies than did the northern population.