Like most things, it's a little more complicated than that. Yes, most of it was about slavery, but not slavery for slavery's sake. In the late 1800's the South was an economic powerhouse, largely due to slavery fueled agriculture vs. new methods of agriculture elsewhere. With that economic status came some measure of worldly significance, something that was quickly being challenged by the rise of the economic cosmopolitans of the North and the significance they were playing in wider trade relations.
And yes, it was about states right to own other human beings and their local sovereignty over their territories against federal authority, but it became more complicated due to the above factors, which were all intertwined in a volatile mixture to maintain and continue their economic and world status.
Contrast that with modern Southern states, which hold almost zero significance to the wider world. Nobody visits the US and goes to Kentucky or Georgia for example. They visit New York or Chicago because of the beautiful architecture or Florida and California for the beaches. Hell, even US citizens never go to these places unless they have to. All of this breeds insularity and a desire to return to a time in history when the South mattered, when they were significant instead not really anything other than the hot, humid South.
Of course, that's not the only reason people brandish the Confederate Flag, to some people it's a family tradition. And some people are truly racist and use it to express that.
That's the thing about symbols, they mean different things to different people.
Disclaimer: I'm not a historian and the views and opinions here are just my observations and understanding of things as I see them as someone that lives in the South (though I consider it the Mid West). I'm open to correction of any and all fallacious or incorrect assumptions here in.