The CSA is waging a war based on what the average person thinks war is like (win a couple of big battles early on and then you win!) and the USA is waging a war based on what war is actually like (the side that has best organized its army and supply chains for the long-term will win).
Basically, the CSA thinks warfare is a "Total War" game - battlefield tactics matter above all else, win a couple of pitched battles, seige a city or two, and call it a day. Strategy? Operations? Logistics? What are those? Meanwhile, the USA thinks warfare veers closer to "Hearts of Iron" - the economy matters, logistics matter, leadership matters. Not a perfect analogy since HoI has its own set of problems of course but you get the idea.
I think that may be a bit unfair though certainly not completely lacking in truth. It seems that the Confederate military has been planning this for years and that they really are a very professional force (at least for now), with a good understanding of logistics and the like - but they're operating under a view of warfare that has more in common with the 19th century than the 20th; where losing one's capitol and a few big battles, is a sure sign that you have lost - and the right thing to do is to give up and just accept the ramifications. I'm sure they were absolutely shocked that actual civilians were attacking them in DC; that sort of thing just wasn't supposed to happen at the time (and it going to lead to some really bad reprisals, just as it did in occupied Belgium in OTL). They seem to have had a similar idea to the Japanese in WW2 in OTL; they fully understood the strength of the Union, it's population and industrial advantages and so forth. But they also thought that the Union military wasn't up to the fight and that the people were decadent and wouldn't have the stomach for the conflict. So a few strong jabs during the opening rounds should be enough to stagger the giant and bring it around to negotiate. Instead, to use one of my Da's favorite phrases, they're about to wake the sleeping giant. Which they SHOULD have known would happen; but the fact that it doesn't is perplexingly understandable when you look at their culture, history and experiences dealing with the US over the past half century.