Exchanging genetic material with another individual seems risky from an evolutionary standpoint, and yet living things across all scales and phyla do so quite regularly. The pervasiveness of such genetic exchange, or recombination, in nature has defied explanation since the time of Darwin1–4. Conditions that favor recombination, however, are well-understood: recombination is advantageous when the genomes of individuals in a population contain more selectively mismatched combinations of alleles than can be explained by chance alone. Recombination remedies this imbalance by shuffling alleles across individuals. The great difficulty in explaining the ubiquity of recombination in nature lies in identifying a source of this imbalance that is comparably ubiquitous. Intuitively, it would seem that natural selection should reduce the imbalance by favoring selectively matched combinations of high-fitness alleles. We show, however, that this widely-held intuition is wrong; to the contrary, we find that natural selection has an encompassing tendency to assemble selectively mismatched combinations of alleles, thereby increasing the imbalance and promoting the evolution of recombination across demes in a structured population. We further show that, on average, selection-driven changes in allele frequencies over time within a single evolving population generate a net imbalance that promotes recombination, and additive fitness effects drive this imbalance. Our findings provide a novel theoretical point of departure from which the enormous body of established work on the evolution of sex and recombination may be viewed anew. They further suggest that recombination evolved and is maintained more as a byproduct of natural selection than as a catalyst.