There's a quote from Shelby Foote's The Civil War in which a captured Confederate soldier was asked why he was fighting in the first place. He responded to his Union captors, "I'm fighting because you're down here."

There's also a scene in the (fictional) film Gettysburg in which a Union captain asks several prisoners what they're fighting for. They ask him the same question and he says, "To free the slaves of course." One of them replies, "I ain't fighting for no darkies one way or the other." Obviously this is not an actual historically documented conversation but I think it points out that the Confederacy didn't see slavery as being the reason they were shooting guns at the other guys.

I think it's really difficult to look back with our modern sensibilities and motivations and try to determine what those people were thinking in a different time and situation. I do know that sectionalism was much more important then than it is now; that people felt loyal to their state more so than to their nation.

The question of why someone who didn't own slaves would fight for slave owners' rights to own slaves is complicated and probably can't easily be answered. I suspect that northern values were seen as incompatible with southern values, combined with heavily biased information about how the north was treating the south, that led to widespread hatred of the Union throughout the south and so many people willing to die fighting their own country.

And as that soldier at the beginning of my comment pointed out, once the Union had already invaded the south and battles had been fought and lives had been ended, there really wasn't anything to do for a poor southerner but fight or be overrun.

Edit: I hope my comment is acceptable, although I know I didn't fully answer your question. I don't have any formal education aside from one undergrad class that discussed the American civil war, but it's a topic I've been interested in for a long time and I've read a fair amount about it.