The soldiers who fought for the south were people's family members, and honoring their memory had evolved into a statement against the cultural erosion that many in the south are upset by. It's possible that plantation owners started the war to protect their slave holdings, but I assure you that no poor unlanded Confederate rifleman died thinking about it.
That doesn't actually fit the facts in explaining the popularity of the Confederate flag as a symbol; the modern popularity of the Confederate flag as a symbol traces directly back to its adoption across the south specifically as a banner of resistance against the civil rights movement, before which it was much less commonly encountered.
My only quibble is that when it's been explained to me in those terms, the explainers often offered it as the only perspective. I can't tell you how many times I've heard "the Civil War wasn't about slavery, it was about states' rights" or "the Civil War wasn't about slavery, it was about the industrial states trying to dominate the agricultural states", etc.
The problem is that every time anyone said "the Civil War wasn't about slavery, it was about X", they were always really trying to say that it wasn't also about slavery. But of course it was also about slavery. There are all sorts of values of X for which one could say, "the Civil War was about slavery, and it was also about X", but there is no value of X that somehow erases the slavery aspect from the origins of the war. It was about a lot of things, but it wouldn't have happened without political disagreements over the continued existence of slavery as a government-protected institution.
There are many people in the south who honor and respect those who died fighting for the CSA, but who still view the war as a great national tragedy in which the south unfortunately chose to stand up for a morally indefensible institution (but may have also been standing up for much more legitimate ideals as well). Those sorts of nuanced views just seemed far less common than the "it wasn't about slavery, it was about X" perspective.
Slavery wasn't even in danger at the time, but Abraham Lincoln was just elected and was very vocal about limiting the spread of slavery to new territories. The southerners were freaking out, believing that if slavery couldn't spread, then it would end up dying out, and all their livelihoods would die out too.
Most of the people in power in the southern were wealthy slaveholders, so they cared a great deal about slavery. For them, it was definitely about slavery.
The non-slaveholding majority weren't as concerned about slavery, but if their state government decided to secede, they felt a loyalty to protect their state. I'd say that for the average southerner who had no slaves, the war was less about slavery and more about a feeling of loyalty towards their state. To me, it seems that the upper class of the southern states dragged their citizenry into war to protect their own way of life, but I don't think that's how the typical southerner viewed it at the time.
This attitude made things very difficult for Jefferson Davis, who was trying to get all the rebellious states to cooperate and work together at a time when they were all screaming about state sovereignty and independence from a federal government.
The average northerner didn't care at all about slavery. At the beginning the northern states had no intention of abolishing slavery. They just wanted to keep the country together and stop the southern states from seceding. Some of the northern states were slave states: they weren't at all in favor of abolishing slavery. Even Abraham Lincoln said that if he could save the union by preserving slavery, he would do so.
Eventually, much later in the war, when there was no hope of the southern states returning voluntarily, Lincoln went ahead and abolished slavery (in the rebellious states only) as a way to hurt them as much as possible. That was really only a way of sticking it to the south and was definitely not a focus of the war for the North.
I definitely would agree that the CSA is looked on in the southern states through rose-colored glasses, and a lot of the more unpleasant realities are glossed over as attitudes change. That's human nature. People who really believe in something tend to reinterpret it as attitudes and opinions change, usually burying the unpleasant aspects in the process.
I suspect that if the southern states had never revolted and seceded, slavery would have slowly dwindled over time and would have eventually been abolished gradually. I don't think that Lincoln would have had the political backing to abolish slavery with the southern states still participating, but he probably would have been able to successfully confine it and make it less appealing.