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 Darwin. 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, thereby opposing the evolution of recombination. We show, however, that this intuition is wrong; to the contrary, we find that natural selection has an encompassing tendency to assemble selectively mismatched combinations of alleles (the products of natural selection), thereby increasing the imbalance and promoting the evolution of recombination. We further show that population dynamics that lead to the fixation of these selectively mismatched genotypes (the process of natural selection) themselves produce an average imbalance that promotes the evolution of recombination. This fact is completely independent of the distribution of allelic fitness effects and is primarily due to the additive component of those effects. Our findings provide a novel vantage point 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 an unavoidable byproduct of natural selection than as a catalyst.