There is some older literature supporting and pushing the idea that anti-DNA antibodies are actually anti-protein antibodies that cross-react with DNA, but there is no fundamental reason to adopt this notion.  As Jing Zhang pointed out, antibodies can potentially react with just about any chemical/biochemical molecular target, based purely on serendipitous affinity of non-covalent chemical bonds between the antigen and “complementarity-determining regions” of the antibody.  (In some cases monoclonal antibodies can even react with disparate antigens not because of true cross-reactivity but probably due to alternative or overlapping binding sites within the CDR.) Nevertheless, the process for production of anti-DNA antibodies in SLE is likely the same as that for induction of any antibodies – the presence in the human of a B cell that happens to have BCRs with an above-threshold affinity for native DNA and which receives “help” for its activation and affinity maturation by T cells. The existence of such B cells is explainable by the huge B cell repertoire and the inefficiency of B cell tolerance mechanisms.   The pathological event, in my opinion, requires the co-presence of autoreactive T cells that had not been tolerized to a peptide ligand derived from a protein that is physically associated with DNA.  Histone-reactive T cells would be obvious candidates, and such T cells could also provide help for autoreactive B cells with receptors for histones or for histone-DNA complexes (nucleosomes/chromatin), which are also common in SLE.  In addition naïve autoreactive T cells would probably also require pre-activation by “professional antigen-presenting cells” presenting the same ligand, but how this happens is more of a mystery. You ask why would this happen: the only (unsatisfying) answer is that the immune system is inherently flawed or imperfect.  Autoimmunity is a side-effect of the evolutionary drive to create an immune system that can anticipate and respond to just about any pathogen.

We can read, previously provided great explanations about biology of the anti-DNA antibodies.

I want to add my understanding of their origin.

In my opinion, it is a similar with recognition of polysaccharide in the conjugate vaccine. Probably, dendritic cells present peptides (histone) to naive helper T cells and they become autoreactive. The peptides that are presented by the dendritic cells to helper T cells are the same peptides that activated the helper T cells when they presented by B cell. Autoreactive T cells help B cells in activation.., than B cells secrete antibodies usually specific for conformational determinants of the native antigen, made up of histone-DNA complexes and produce anti-nucleosome/ anti-DNA antibodies.

In other words, single B cell specific for a native epitope (nucleosome) may endocytose a protein and present multiple different peptides to different helper T cells, but the resultant antibody response remains specific for the native antigen.