The maintenance of sexual reproduction in eukaryotes is still a major enigma in evolutionary biology. Meiosis represents the only common feature of sex in all eukaryotic kingdoms, and thus, we regard it a key issue for discussing its function. Almost all asexuality modes maintain meiosis either in a modified form or as an alternative pathway, and facultatively apomictic plants increase frequencies of sexuality relative to apomixis after abiotic stress. On the physiological level, abiotic stress causes oxidative stress. We hypothesize that repair of oxidative damage on nuclear DNA could be a major driving force in the evolution of meiosis. We present a hypothetical model for the possible redox chemistry that underlies the binding of the meiosis-specific protein Spo11 to DNA. During prophase of meiosis I, oxidized sites at the DNA molecule are being targeted by the catalytic tyrosine moieties of Spo11 protein, which acts like an antioxidant reducing the oxidized target. The oxidized tyrosine residues, tyrosyl radicals, attack the phosphodiester bonds of the DNA backbone causing DNA double strand breaks that can be repaired by various mechanisms. Polyploidy in apomictic plants could mitigate oxidative DNA damage and decrease Spo11 activation. Our hypothesis may contribute to explaining various enigmatic phenomena: first, DSB formation outnumbers crossovers and, thus, effective recombination events by far because the target of meiosis may be the removal of oxidative lesions; second, it offers an argument for why expression of sexuality is responsive to stress in many eukaryotes; and third, repair of oxidative DNA damage turns meiosis into an essential characteristic of eukaryotic reproduction.