If any part of this premise is wrong, please correct me.

The constituent States of the Confederate States of America submitted a variety of declarations of succession/independence to explain their rupture from the Union, and to oversimplify just a bit, it was because they thought Abe Lincoln was gonna kill slavery and they weren't gonna stick around to give him the chance. That's pretty well supported, yeah?

Well, the constituent States and the constituent population are two different things, whose interests did not always align. The governments of those states, and later that of the CSA, were in many ways beholden to the rich plantation owners and other wealthy interests; poor Southern whites did not own slaves, and though undeniably better off than Black Americans, they often lived in brutal poverty. Why therefore did average white men fight for a government that did not have their interests at heart?

Is it really as simple as LBJ suggested, that a white man will let you pick his pocket if you convince him he's better than the best Black man? Pick his pocket even of his life? Or were there more complicated motives for the average private soldier in the CSA's army?

(Please understand I in no way endorse the Lost Cause myth; the CSA was a racist monster that deserved to die.)