Common knowledge of over a century has it that monozygotic and dizygotic twinning events occur by unrelated mechanisms: monozygotic twinning ‘splits’ embryos, producing anomalously re-arranged embryogenic asymmetries; dizygotic twinning begins with independent ovulations yielding undisturbed parallel embryogeneses with no expectation of departures from singleton outcomes. The anomalies statistically associated with twin births are due to the re-arranged embryos of the monozygotics. Common knowledge further requires that dizygotic pairs are dichorionic; monochorionicity is exclusive to monozygotic pairs. These are fundamental certainties in the literature of twin biology. Multiple observations contradict those common knowledge understandings. The double ovulation hypothesis of dizygotic twinning is untenable. Girl–boy twins differ subtly from all other humans of either sex, absolutely not representative of all dizygotics. Embryogenesis of dizygotic twins differs from singleton development at least as much as monozygotic embryogenesis does, and in the same ways, and the differences between singletons and twins of both zygosities represent a coherent system of re-arranged embryogenic asymmetries. Dizygotic twinning and monozygotic twinning have the same list of consequences of anomalous embryogenesis. Those include an unignorable fraction of dizygotic pairs that are in fact monochorionic, plus many more sharing co-twins’ cells in tissues other than a common chorion. The idea that monozygotic and dizygotic twinning events arise from the same embryogenic mechanism is the only plausible hypothesis that might explain all of the observations.