Hypertensive disorders of pregnancy (HDP: pregnancy-induced hypertension, preeclampsia, eclampsia) affect approximately 10% of human births. Women are at increased risk for HDP during their first conception; and/or when the conception is with a new partner (new paternity); when conception occurs very shortly after the beginning of their sexual relationship. A primary cause of preeclampsia is the defect of the normal human-specific deep endovascular invasion of trophoblast, which is a consequence of the nutritional demands of growth of the human fetal brain. The occurrence of preeclampsia represents a reproductive disadvantage unique to humans compared with other mammals. As such, it may have played a significant role in shaping human reproduction and, therefore, human sexuality. This deep implantation/preeclampsia phenomenon may explain many anthropological mysteries of human sexuality that do not exist in other mammalian species (and primates). These include: very low fertility rate, concealed ovulation, all year long 'apparent-waste-of-efficiency' sexuality, absence of sperm competition in human females at the time of conception, and the unexplained testicle size in human males compared with relevant primates. Further, this deep trophoblastic implantation (and its failure in preeclampsia) in humans might be a decisive condition of hominization between great apes and all the other Homo genuses. This frontier might even have occurred inside these Homo lineages: because of their relatively small brains, the first species of Homo might not have presented the deep trophoblastic invasion described in Homo sapiens.