Molecular dissection of meiotic recombination in mammals, combined with population-genetic and comparative studies, have revealed a complex evolutionary dynamics characterized by short-lived recombination hotspots, whose exact location is determined by the DNA-binding protein PRDM9. To explain these fast evolutionary dynamics, a so-called intra-genomic Red Queen model has been proposed, based on the interplay between two antagonistic forces: biased gene conversion, mediated by double-strand breaks, resulting in hotspot extinction (the hotspot conversion paradox), followed by positive selection favoring mutant PRDM9 alleles recognizing new sequence motifs. Although this model predicts many empirical observations, the exact causes of the positive selection acting on new PRDM9 alleles is still not well understood. In this direction, experiment on mouse hybrids have suggested that, in addition to targeting double strand breaks, PRDM9 has another role during meiosis. Specifically, PRDM9 symmetric binding (simultaneous binding at the same site on both homologues) would facilitate homology search and, as a result, the pairing of the homologues. Although discovered in hybrids, this second function of PRDM9 could also be involved in the evolutionary dynamics observed within populations. To address this point, here, we present a theoretical model of the evolutionary dynamics of meiotic recombination integrating current knowledge about the molecular function of PRDM9. Our modeling work gives important insights into the selective forces driving the turnover of recombination hotspots. Specifically, the reduced symmetrical binding of PRDM9 caused by the loss of high affinity binding sites induces a net positive selection eliciting new PRDM9 alleles recognizing new targets. The model also offers new insights about the influence of the gene dosage of PRDM9, which can paradoxically result in negative selection on new PRDM9 alleles entering the population, driving their eviction and thus reducing standing variation at this locus.