You'd be wrong, there. I think I have a pretty good idea of why the average southern soldier was fighting, and I would never say that he was fighting for slavery, at least in his mind. He was fighting for his home, his community, his state, and for his interpretation of his rights. You, on the other hand, appear to be simply baffled by anyone who remained loyal to the United States and answered the call of the flag.
Yes, it does perplex. The only way I could see doing it would be if I were drafted. I could not/would not volunteer to fight against any state(s) that wanted autonomy, regardless of their reason, and even if I thought the it was for the wrong reason. It a southern thing, if you have to force it, it aint't no good.