Why shouldn't libertarians support the Confederacy? In short, because the Confederacy itself was not very libertarian.
In addition to being founded explicitly to protect the slave trade in America, the Confederacy conscripted soldiers, inflated its money supply during the war, and played host to many civil liberties violations.
But that's not to say that the Union was much better, as Jason Kuznicki (@jasonkuznicki) explains.
Kuznicki is a Research Fellow at the Cato Institute and is editor of Cato Unbound.