Mutation in the germline is the ultimate source of genetic variation, but little is known about the influence of germline chromatin structure on mutational processes. Using ATAC-seq, we profile the open chromatin landscape of human spermatogonia, the most proliferative cell type of the germline, identifying transcription factor binding sites (TFBSs) and PRDM9-binding sites, a subset of which will initiate meiotic recombination. We observe an increase in rare structural variant (SV) breakpoints at PRDM9-bound sites, implicating meiotic recombination in the generation of structural variation. Many germline TFBSs, such as NRF1, are also associated with increased rates of SV breakpoints, apparently independent of recombination. Singleton short insertions (>=5 bp) are highly enriched at TFBSs, particularly at sites bound by testis active TFs, and their rates correlate with those of structural variant breakpoints. Short insertions often duplicate the TFBS motif, leading to clustering of motif sites near regulatory regions in this male-driven evolutionary process. Increased mutation loads at germline TFBSs disproportionately affect neural enhancers with activity in spermatogonia, potentially altering neurodevelopmental regulatory architecture. Local chromatin structure in spermatogonia is thus pervasive in shaping both evolution and disease.