"That leads to the question of why would all of those non-slave-owning citizens march off to die for something they didn't have anyway?"
Some time ago, I ended up in a long discussion here on this topic, and it forced me to look further and learn more. What I found challenged what I'd long believed. For example, I long believed that slaveholders were a teeny-tiny percentage of the population and that impoverished Confederate soldiers were forced to fight a war for the wealthy few. But, in checking further, I came across articles that said the percentage of slaveholders was larger. In addition to plantation owners with many slaves, some families would purchase, say, one slave, and small-time farmers might hold a few slaves. So, even the people who did not personally "own" a slave often were connected to people who did - sometimes in their own families. The purchase of a slave was a big investment, so one reason slaveholders did not want to free their slaves was financial.
Another reason was that generations of people were accustomed to a way of life that involved slavery, and they didn't want it to change. Plus, as the Southern Democrats (who controlled those states) declared in their written reasons for secession, they feared what might happen if the slaves were freed. There were still some slaves held up North at the time (if what I read is correct), but in a couple of southern states, the slaves outnumbered the free people.
Some people believe they seceded over a tariff, but I don't recall seeing a tariff mentioned specifically in writing as a reason for secession. But, Southern Dems could see their power in the federal government would diminish, if more "free" states were admitted to the union.
Below are the links I kept for the official documents. As you noted before, these documents give slavery as the main reason for secession. Then, when the CSA wrote its constitution, they enshrined slavery in it. Crazy. Sheesh, those poor slaves...
Secession Acts of the Thirteen Confederate States
Declarations:
South Carolina
Mississippi
Georgia
Texas
Resolutions: