Howdy.
People who point out that many Southern soldiers did not own slaves are doing so not to make a historical point but to support the argument that the Civil War was not fought over slavery. You will never win an argument with them about that because what they are saying is true, but their conclusion is false.
The best response in my opinion is to say "True, but why is that important?". Then they must expose their real motive in making the argument and you can easily argue with that.
The real reasons that individual white Southerners fought is too complex for a hallway conversation. It is a rich tapestry made up the cumulative stories of all the Southern people at a particular place and time. It reaches across the South into every city, town, farm and plantation, and touches on all of the individual lives of the people who lived, worked, loved and lost in a (to us) crazy world that went crazy around them. You cannot paint them all with the same brush.
Although it is clear that Southern States seceded to retain the "State's Right" to protect and expand the practice of human chattel slavery, the reasons that individual Southerners fought include all of the reasons that folks fight in any war along with reasons unique to the times.
Historically wars are quite common - for some reason societies have no problem getting people to fill out their armies. Soldiers end up in the army for all sorts of reasons. And once in the army, people fight for reasons far different from the ones that brought them there.
From my reading, the desire for secession was not universal among the people, especially initially. There were distinct waves of enlistment in 1861 and 1862. There are all sorts of reasons to enlist, and many were related to the perceived threat to slavery - fear of "bottom log on top" - racial fears of mixing of the races - fear of economic ruin - general acceptance of the concept of **** - and these feelings were by no means restricted to slave owners. But these were just some of the reasons that people ended up in the army.
As events progressed and it was clear that the Southern states were going to be invaded by Northern armies, many people did what people have always done when their society is threatened and joined up to defend it. When threatened, right or wrong becomes less clear, and even less important. Shelby Foote said Southerners fought because the Northerners where "down here" and I'm sure that was true and enough for may Southerners.
It is also important to note when discussing reasons Southerns fought, that a great many Southerners did not fight, or even fought for the North.