A good source for this, which I encourage you to read if the subject interests you, is the book For Cause and Comrades: Why Men Fought in the Civil War by James M. McPherson. As the title suggests, it's a survey of motivations and descriptions of why soldiers on both sides fought in the Civil War, taken from a sample of the surviving letters of 1,076 Civil War soldiers. McPherson sampled the soldiers proportionately (647 Union soldiers, 429 Confederate soldiers - he actually deliberately over-sampled the Confederate soldiers a bit), and within that sample, they were selected by age range and geographic location, to represent the age range and geography of the actual Civil War servicemen.

Through this sample, McPherson characterizes the Southern motivation: "[M]ost Southern volunteers believed they were fighting for liberty as well as slavery."

McPherson writes that the rhetoric about liberty and independence were probably more common in Confederate letters, but the two concepts were often intertwined. Southern soldiers understood that "liberty" included the freedom to preserve slavery.

Early in the book, McPherson recounts an anecdote about the Steedman brothers from South Carolina, one a Naval officer who remained loyal to the Union. His Confederate brother wrote to him, shocked that he would be "a Traitor to his Mother County" of South Carolina and "allow Northern principles to contaminate his pure soul". The Confederate Steedman believed that Northern "fanatics" determined "to interfere with our domestic affairs" of slavery and deny Southerners the right "to keep our slaves in peace & quietness" is what must have turned the Union Steedman against his home. (The other Steedman replied that he had always been "a Union man" and "my duty to flag & country" is what motivated him to stay loyal.)

While it might not be intuitive to think that non-slaveholding Southerners would want to fight for slavery, since slavery was, as you said, dominated by the upper class, there were more considerations than just ownership. Although even in that, a considerable amount of white Confederate state families did own people as slaves—between a low of 20% of white families in Arkansas, to a high of just under 50% in Mississippi.

But beyond "taking away their property", there were other fears and considerations related to slavery. A big one was the threat of "servile insurrection". It really can't be underestimated at how pervasive the fear was that if the "black Republicans" and abolitionists got into power, they would encourage emancipation, which would start a race war. This wasn't anything new, but was a fear that went back decades. Even President Millard Fillmore had once written about it in his State of the Union Address, although the section was taken out before the address was delivered and published. In it, he predicts a race war egged on by Northern "agitation" that was sure to end in the extermination of one race or the other in the South, and probably the black race. But whoever won, it would be bloody, so he encourages a scheme to begin deporting enslaved people to Africa. And remember Fillmore was from the North. The Southern fear of this was even worse.

Another fear was that, if the Republicans ever succeeded in emancipation, it would mean equality of black people. And equality meant that white people would have to compete for jobs against formerly enslaved people, which was humiliating, and would also drive wages down to next to nothing. Slavery allowed even the lowliest white person to not be on the lowest rung of the social ladder. McPherson quotes a Louisiana artilleryman in an 1862 letter (slur edited - slurs were used rather liberally when talking about the subject):

"I never want to see the day when a negro is put on an equality with a white person. There is too many free n****rs ... now to suit me, let alone having four millions."

Miscegenation was another fear of Southerners. The end to slavery meant that there would no longer be a pure white race in the South, but that it would usher in a mixed race society. (This continued to be a fear after the war and was a primary justification for segregation.) This race mixing would mean that their descendants would all be "part slave". A Wisconsin soldier during the 1864 Atlanta campaign recalled this conversation (again, slur edited):

"Some of the [Union] boys asked them what they [Confederates] were fighting for, and they answered, 'You Yanks want us to marry our daughters to the n****rs.'"

And another fear was the loss of political control. There were so many black Southerners, that if they became free and were ever able to vote, they would hold the political offices. And with how the white people had treated the black people, the white people feared that the black people would do the same or worse to them. And that, of course, would be very, very bad.

These types of sentiments didn't spring up out of nowhere. Both the political class and the press had been promoting these fears for years before the Civil War, and it only got worse during the 1860 election campaign. If you want to see a good cross-section of primary sources, then seek out the book Southern Editorials on Secession edited by Dwight Lowell Dumond. Or for a narrative account, you might try Fanatics and Fire-Eaters: Newspapers and the Coming of the Civil War by Lorman Ratner and Dwight L. Teeter Jr. Throughout 1860 and up until Fort Sumter, the Southern press was essentially running a fear campaign that the Republicans and Abraham Lincoln would upend Southern society, and it would be the doom of the white man. Thus, it was their duty to fight for Southern society, and the liberty of the South.

Not every newspaper agreed. There were plenty of Unionists who, in fact, believed the best way to preserve slavery and preserve white Southern society was within the Union, and to fight in Congress. Walking away and starting a war was sure to doom slavery even faster. But in those days, just about every town had both a "Union" newspaper and a "Secession" (Southern Democrat) newspaper, so even if you were a Unionist, you were surely exposed to the secessionist rhetoric, too.

Beyond newspapers, there were also many pamphlets published. A good source for these is the book Southern Pamphlets on Secession, November 1860 - April 1861, edited by Jon L. Wakelyn. One of the pamphlets reprinted is entitled "The Interest in Slavery of the Southern Non-Slaveholder" which enumerates ten reasons for non-slaveholders to want to preserve slavery. I won't go over them all here (feel free to read the pamphlet for yourself), but the gist of them is that the end of slavery would be the "degradation" of the white race to an inferior position to black Southerners, that it would be bad for white people's finances, and that preserving slavery gives white non-slaveholders the chance to work their way up and become wealthy slaveholders themselves one day.

The other pamphlets in the Wakelyn book are mostly reprinted speeches from Southern politicians, or from clergymen arguing along similar lines, championing secession to preserve slavery and the Southern way of life.

The cause of liberty was also commonly cited among Confederate soldiers' letters, and McPherson provides many examples. Many soldiers on both sides of the conflict would evoke the Founding Fathers and Revolutionary War. As just a few examples on the Confederate side, an Alabama solider wrote:

"How trifling were the wrongs complained of by our Revolutionary forefathers, compared with ours".

A Kentucky soldier wrote:

"[George Washington] set us an example in bursting the bonds of tyranny."

A South Carolina soldier wrote:

"Times may grow a great deal worse than they now are, and still we can stand it—And even then not go through what our Grandparents went through, when they were struggling for the same thing that we are now fighting for."

And after learning of the loss at Vicksburg, a Georgia soldier wrote:

"Let us not despair....Our forefathers were whipped in nearly every battle & yet after seven years of trials & hardships achieved their independence."

But even the cause of liberty was often wrapped up in slavery, as McPherson writes:

"[Soldiers from slaveholding families] tended to emphasize the right of property in slaves as the basis of the liberty for which they fought. This motive, not surprisingly, was much less in evidence among nonslaveholding soldiers."

As the war went on, there were also appeals to camaraderie—fighting alongside other young men from your community—that is evident in any war. But mainly, the motivations at the outset were very much slavery and liberty, and often both at the same time. This ebbed and flowed, with the slavery rhetoric increasing in reaction any time the Union took anti-slavery action (particularly with the Emancipation Proclamation and its announcement three months earlier). Liberty was often emphasized after losses in major battles.

Yet, white Southern identity had long understood their "liberty" and "freedom" to include the freedom to own slaves. Their identity couldn't really be separated from slavery. When that institution and social order was perceived to be under threat, they answered the call to protect it. The young men who served the Confederacy had been exposed to pro-slavery, anti-abolition, even anti-Northern rhetoric their whole lives. And pro-abolition, anti-slavery publications and organizations had been banned and suppressed. From 1860 to the beginning of the war, the rhetoric was amped up even more. It wasn't difficult to get white Southerners to fight for slavery, liberty, and their Southern (slavery-based) way of life.