DNA in all living systems shares common properties that are remarkably well suited to its function, suggesting refinement by evolution. However, DNA also shares some counter-intuitive properties which confer no obvious benefit, such as strand directionality and anti-parallel strand orientation, which together result in the complicated lagging strand replication. The evolutionary dynamics that led to these properties of DNA remain unknown but their universality suggests that they confer as yet unknown selective advantage to DNA. In this article, we identify an evolutionary advantage of anti-parallel strand orientation of duplex DNA, within a given set of plausible premises. The advantage stems from the increased rate of replication, achieved by dividing the DNA into predictable, independently and simultaneously replicating segments, as opposed to sequentially replicating the entire DNA, thereby parallelizing the replication process. We show that anti-parallel strand orientation is essential for such a replicative organization of DNA, given our premises, the most important of which is the assumption of the presence of sequence-dependent asymmetric cooperativity in DNA.