I've no idea whether Howell believed it or not at the time he was talking, but he's being rather less than candid. If the CSA fought for any cause except slavery, then they spent four long years doing everything humanly possible to prove to posterity that they did. It's probably the exhaustively documented thing about the Confederacy.

While I don't want to discourge follow-ups, we have a FAQ section on just this subject. The best place to start would be with /u/georgy_k_zhukov 's mega-post on the subject.

One may plead that individual soldiers don't know their politics, as Howell makes a gesture toward, but that's selling them very short indeed. Ordinary people are ordinary, sure, but we shouldn't presume them ignorant or fools. We especially shouldn't do so over a crucial political issue which had been debated in public at length for the entire history of the United States to date. Among other things, the extension of slavery was the central issue of the 1850s and the 1860 election. One party, the Republicans, avowed a platform of restricting slavery to the states where it already existed and not admitting another slave state to the Union. The other party, the Democrats, split between those who believed that the federal government should actively institute slavery in the territories by means of a slave code and those who did not. The election of the Republican candidate, who they understood as hostile to slavery, was the immediate cause of the secession of the seven most enslaved states. The Upper South, bar the four least enslaved states, tried to bolt when it became clear that Lincoln would not just let the Lower South go in an explicit act of solidarity with fellow slaveholding states.

Nor should we let ordinary soldiers off the hook for joining the military of a nation dedicated to the preservation and extension of slavery and so actually fighting to preserve and extend the institution, whatever mental reservations they might have had. The Confederate military wasn't that of an ordinary nation where people might just sign up for whatever reason and then find politics change and they're stuck. It's the purpose-built engine of the slaveholding insurrection, literally created in that moment and to fight that war.

But to answer your question: there are no rights the North had that the South did not. As a practical matter, it's the other way around. The United States constitution and the federal government from ratification until 1865 granted to the slave South (the South is just the slave states, no more or less) tremendous advantages for slavery which it had prosecuted aggressively against local autonomy in the free states for just as long, albeit with considerably increased intensity as the antebellum went on. Among many other things, including the extra representatives granted to the South via the 3/5 rule and the section's population-agnostic parity and then near-parity in the Senate, Southerners had the right to go into states where slavery was illegal and take back any slave that had escaped to there. That was literally a selling point of the Constitution for the slave states.

In 1850, that right was dramatically expanded so that ordinary northerners faced severe criminal penalties for aiding and abetting fugitive slaves and were subject to on-the-spot conscription into slave-catching, per the new Fugitive Slave Act. That act was passed to deliberately overrule various personal liberty laws that free states had enacted to ensure due process and otherwise prevent southerners from just kidnapping any black person they saw and which limited the requirement that of state-level officials cooperate with slave catching. This law was passed not at the agitation of tyrannical Yankees demanding federal supremacy for its own sake, but rather at the insistence of Southerners and as part of the price for their tolerating the admission of California to the Union as a free state.

Short of literally abolishing the states, it's hard to imagine a law more perfectly antagonistic to state's rights...if we assume that's an actual interest in itself. The problem is that it's not. State's rights isn't a cause, but rather a method. Unless one is perverse, one prefers local autonomy because one expects it to deliver outcomes (at least near home) which one finds more congenial. Nobody wants to pass something that matters to them over to a level of government they consider incompetent or malignant. So even if there's a principled position that state power is just in general better, it's better for specific reasons and saying "state's rights" tells us none of them. We must always ask state's rights for what?

What we see all down the antebellum is that embrace of state's rights is instrumental and circumstantial. Everybody understands it as a method by which you secure outcomes, not the end itself. That's true when South Carolina wants to nullify a tariff that it believes cuts into the profits of its slave-grown agriculture in the 1830s. It's just as true when Massachusetts says "state's rights!" to protest Jefferson's embargo, or when Jefferson himself uses the concept to oppose the Alien and Sedition Acts. When Wisconsin went and nullified the Fugitive Slave Act in the late 1850s, no less a southerner than Dred Scott author Roger Taney slapped them down and protests in the South were conspicuous only in their absence. The primacy of national and state power change places every time an issue appears to be going against someone on the federal level.

Compared to all this, the North's insistence that the slave states should abide by the results of an election contested fair and square is downright circumspect. It was considerably less than the South had demanded and gotten, time and time again, for the decades prior in an unbroken, nearly perfect streak of victories. But the South understood that slavery could never be safe in the Union unless the slave states had control domination of that Union, particularly when one of their own wasn't in the White House. Lincoln's election presented an existential, if possibly long-term threat to slavery's security.

Since 1800, at the latest, that was the section's red line. If slavery and the Union came into conflict, which seemed a relatively remote prospect way back then, then slavery came first. Without slavery there's no Civil War and, indeed, no South at all. Slavery is the sole fact, as understood by people at the time, which makes places and things Southern right down to the point where when it appears that massive election fraud has ensured territorial Kansas will institute slavery, the proslavery side crows that the territory has joined the section.

Howell himself tips his hand a bit on that point. The rights curtailed after the war, during Reconstruction, were curtailed because the white South was doing everything in its power to preserve as much of slavery as they could manage. The fate of the freedpeople was understood in the South as the key issue of the war. By reducing them to slavery in all but name, they could turn their loss into a win. Up in the free states, they looked at the same facts, agreed, and for a brief moment prosecuted an aggressive campaign to ensure slavery would not return. That's the horror of Reconstruction which the white South (mostly, there are some dissenters) fought. From their eventual (if not absolute) victory, we get the line that the North won the war, but the South won the peace.