You ask a great question, but also a complex one. At its most basic, this narrative bias in what you might call the southern-influenced historiography’s emphasis on state’s rights as the root of the American Civil War was born the day of Lincoln’s election as President. Prior to Lincoln’s 1861 inauguration, the leaders of what would become the Confederate States of America had argued that Lincoln’s election meant a war on slavery and by extension the south’s way of life (i.e., their rights as individual states to operate as they pleased). This was, of course, an illusion, as Lincoln didn’t wage war on southern institutions of slavery directly until the Emancipation Proclamation was announced in late-1862. Yet the south saw Lincoln’s election as a harbinger of a rising abolitionist tide, and pushed hard for secession as a result. Although their language of separation was always rooted in slavery, they draped it in this lofty rhetoric of state’s rights to give it legitimacy. So the conflict was born in the midst of this argument over the narrative of the struggle itself: an issue that was, at its heart, slavery, but was cloaked in talk of state’s rights.

Now, just to briefly interject. As a historian I feel that a conflict as massive and complex (on a political, social, racial, and economic level) can’t be boiled down to just one factor. Yes, slavery was the hot-button topic that led to the Civil War, and was undoubtedly the main issue that brought the conflict to a head. But there had been a struggle in American politics that went back to the founding of the nation itself over big vs. small government. Hamilton and Jefferson famously quarreled over this issue (see also: the National Bank), so there was an established, root-conflict at the heart of the United States that had little to do with slavery. When the slavery issue blossomed into a mortal struggle over the soul of the United States in the 19th century, this old argument over big vs. small government resurfaced, and established tensions about whether the government had the right to enforce economic and civil policies on the states sprang back to life.

I bring this up because it is important to understand where OP’s friend’s biases come from, because it actually pre-dates slavery, the Civil War, and even the country itself. THAT’S what makes this issue so interesting to discuss, because at the foundation, the American Civil War was a struggle over slavery, and whether it would continue or start its slow death in this country. What the C.S.A. did, however, was dress up their struggle in this older, established conflict between the states and the central government: it fit their narrative and conveniently protected their ability to maintain the institution of slavery. After the Emancipation Proclamation, the need to cling to this “state’s rights” narrative became even more important for the south, because they had to sell their struggle to Britain and France (who they hoped would recognize them) not as a fight for slavery, but as a noble struggle for autonomy.

And here’s the important part, in my opinion. After the war, southerners had to reconcile the admittedly brave and impressive feats of their soldiers with the cold reality of what they were fighting for (to protect the institution of slavery). As a result, this state’s rights narrative was a lifeline. The soldiers and generals who had sacrificed so much, and shown so much bravery needed to be redeemed so that these southern communities could celebrate their past. The easiest way to do that was to adopt what you might call “the party line” of the Confederacy, and claim that these brave soldiers and their noble generals didn’t fight to oppress others (as indeed they did, whether they believed that at the time or not), but rather to PROTECT their homes and families. When talking about brave uncle, dad, grandpa, etc. who fought in the war, this is a much more pleasant and palatable story. It allowed the south to celebrate this portion of their past without confronting the ugly reality underpinning it.

Sorry I don’t have any sources to link on this – my distillation of the topic is sort of an amalgam of a number of other historians who have written on the subject in prefaces, etc. Jay Winik does talk about this a little bit in his book ‘April, 1865’ in his introductory chapter.

EDIT - GRAMMAR

I apologize if this is an inappropriate answer but I think your question is more a current education/"cultural" question than a history question because you're asking why southerners are still teaching that the civil war was fought over state's rights. Most, if not all, active Civil War historians agree that the Civil War was fought over slavery or, at the very least, the state's rights to own slaves (just read the article of cessation.) History is ever changing and simply put, she learned this because that's what her teachers were taught - depending on how long ago they attended school. After graduating teachers are not under any obligation to keep up on current research, I'm not a Civil War historian but I did get my master's from a moderately sized university in the south where I was required to take courses on southern history and can say that no one actually teaches this any more. It's like global history vs western civ., you'd be hard pressed to find any school that still teaches the latter.

I think reading Blight's Race and Reunion would be beneficial to better understand the Lost Cause mindset, the politics of memory, and why the Civil War was taught differently in the southern states than in others.

Edit: I would add that it's not still being taught that way. No text book I've run across in teaching 3 sections of US to 1876 has said anything about state's rights, I graduated from high school 10 years ago and even then I was told it was fought over slavery. So, if this is what your friend has learned her teacher was expressing her personal opinion as fact but I wouldn't assume that this is wide spread. Again, Blight's books would better explain why this particular individual feels that it was over state's rights vs slavery.

One thing that helps provide at least one perspective from that time is the "Corner Stone Speech" by the Confederate Vice President, Alexander Stephens. The difference between the views expressed in the Corner Stone speech and the view that the Civil War was about state rights, indicates that the state rights view may have become more prevalent after the war.

"Our new government is founded upon exactly the opposite idea; its foundations are laid, its corner- stone rests, upon the great truth that the negro is not equal to the white man; that slavery subordination to the superior race is his natural and normal condition. This, our new government, is the first, in the history of the world, based upon this great physical, philosophical, and moral truth."

http://teachingamericanhistory.org/library/document/cornerstone-speech/

http://www.csmonitor.com/Books/chapter-and-verse/2015/0708/The-famous-1861-Cornerstone-Speech-that-aimed-for-hard-truths-about-the-Confederate-battle-flag-video

There are some excellent answers in here but one explanation I see skimped over is that there wasn't exactly a consensus about this during the war. In 1865 South Carolina had to assemble its state senate to draft a new constitution. A reporter visiting there, Sidney Andrews, wrote extensively about the political arguments and debates going on. Large parts of the senate meetings were spent on abolishing slavery and whether or not the war was even over slavery. He also details the bitter divides between up-country whites and low-country planters, including discussions about who was to blame for dragging everyone into the war.

You can find his book free online here. It's also available on Amazon, I stumbled on a copy in an old book shop.

The whole book is amazing, he almost gets lynched in Georgia just for suggesting a white guy should maybe not shoot a freedmen over a stupid argument. He does a very good job of exploring the differences between the public rhetoric of war propaganda and then what Southerners will say to him in private about it. As a Southerner I liked it because Andrews was simultaneously keenly interested in the politics of the South but also wanted to portray them as people. It would be a good read for your friend.