August Weismann proposed that genetic changes in somatic cells cannot pass to germ cells and hence to next generations. Nevertheless, evidence is accumulating that some environmental effects can promote heritable changes in the DNA of germ cells, which implies that some somatic influence on germ line is possible. This influence is mostly detrimental and related to the presence of oxidative stress, which induces mutations and epigenetic changes. This effect should be stronger in males due to the particular characteristics of sperm. Here, we propose the hypothesis that females are able to avoid males with oxidatively damaged DNA in the germ line by using oxidative-dependent (pre- and post-mating) signals. This new hypothesis may shed light on unsolved questions in evolutionary biology, such as the benefits of polyandry, the lek paradox, or the role of sexual selection on the evolution of aging.