The esteemed Kevin Levin has a post about the narrow appeal of the Sons of Confederate Veterans. It's really about the neo-confederate movement, and not about civil war reenacting, but as a reenactor who does not dress up like a confederate (or anyone else from the Late Unpleasantness of Northern Aggression Between the States), I feel obligated to answer the question in his title.
In some ways I seem like a perfect candidate for confederate reenacting -- I'm from Virginia (Northern, but my Dad was from Richmond and my mom is enamored with the South, so I grew up in a more 'Southern' environment than most kids in Fairfax County), I have been fascinated by the civil war on and off since gradeschool, and I like dressing up in funny clothes on the weekend. I have confederate ancestors (at the moment I remember a cavalrymen who served under Stewart, but there were others as well) and the idea of connecting to them through reenacting's odd roleplaying is appealing. Moreover, I believe that reenacting can be valuable.
But there are two reasons I haven't thrown my kepi in and joined up with the boys in gray.
1) Confederate reenacting (and civil war reenacting in general) is wrapped up in a way of remembering the war -'brother against brother', if not the Lost Cause proper-that I do not agree with. In both cases, slavery is minimized as a cause of the war, in the interest of vaporizing those who fought. I remember sitting and eating oysters (which were delicious) with a rather authentically clad Confederate reenactor, who said that most confederate soldiers did not own slaves*. The learned Andy Hall has dealt with this; showing that a huge proportion of confederate soldiers had a direct interest in slavery, and that those that didn't had a powerful indirect interest. And this sort of thing is common to hear from confederate reenactors. Union reenactors are often too interested in remaining on good terms with their counterparts on the other side, so they will (like the North 100 years ago) avoid the slavery issue entirely. As I have mentioned before, I do not think this does any honor to the dead or any good for the living.
So what you have here is a reenacting community that, rather than educating the public about the past, perpetuates a falsehood; as I've mentioned before this is a breach of the implicit contract between reenactors and the public. The reenactor must be a student of history, and as such must be constantly curious. Dismissing the last 40 years of historical scholarship as PC Bullcrap, as I have heard some reenactors do, is a breach of our duty to be curious students of history and in turn to pass on that knowledge to the public. So that's why I don't reenact the civil war, either as a confederate or a union soldier.
It must be said that these issues, though very ingrained in the reenacting community, are not necessarily essential to it. I can imagine a world where civil war reenactors acknowledge the context of the war, and reenact out of a love of history rather than their conception of their heritage.
But this is unlikely, and in some ways beside the point, due to my second reason for not enlisting in a mock Army of Northern Virginia"
2) It is hard to reenact as someone without celebrating them in some way. Reenacting is about humanizing and presenting the past to the public. Telling someone's story is intrinsically sympathetic. It is part and parcel with most reenacting groups to be something of an advocate for those they represent; we medieval reenactors emphasize that the middle ages were not some vast dung-heap, the Rev War Redcoats and Loyalists remind people that there was another side of the Revolution War, etc. But the urge to humanize can also lead to a softening of the edges of history's unpleasantness. Partly out of identification with those we portray, partly to seem less like weirdos, reenactors can minimize the unpleasant deeds that those they portray did.
Moreover, decency prevents a truly accurate portrayal of some things in history, including the confederate army. As my spouse said, she's always tempted to ask the confederates 'where are you slaves?' -- the body servants, teamsters for the caissons and laborers to dig trenches. Showing such things in a reenacting event would be both ...difficult to arrange (I'm not imagining many volunteers) and offensive to the public. Thus a certain sanitization of the past is part and parcel with reenacting. In the case of the confederacy, the likeness is so distorted by this sanitization that I cannot participate in it.
*Ironically, the unit being portrayed was from Amelia County, Virginia, which as this map (also found in PDF here) shows, had nearly 3 times as many slaves as free people, the second highest ratio in the State.
PS: On a frivolous note, the US regulars have the best uniforms - much more flattering than gray and butternut: