Brain microstructural asymmetry can provide more direct causal explanations of functional lateralization than can macrostructural asymmetry. In this study, we discovered two new types of microstructural asymmetry that help to bridge the gap between macrostructural asymmetry and functional lateralization. Myelin-related asymmetry was prominent in the back brain, and axon-related asymmetry occurred in both the front brain and the back brain. These asymmetries early in development indicate that white matter is more mature and more myelinated in the left back brain, providing an explanation for the leftward lateralization of language and visual functions. The asymmetries continue to increase throughout childhood and adolescence.