Embryonic development in mammals has evolved a platform for genomic conflict between mothers and embryos and, by extension, between maternal and paternal genomes. The evolutionary interests of the mother and embryo may be maximized through the promotion of sex-chromosome genes and imprinted alleles, resulting in the rapid evolution of postzygotic phenotypes preferential to either the maternal or paternal genome. In eutherian mammals, extraordinary in utero maternal investment in the brain, and neocortex especially, suggests that convergent evolution of an expanded mammalian neocortex along divergent lineages may be explained, in part, by parent-of-origin-linked gene expression arising from parent-offspring conflict. The influence of this conflict on neocortical development and evolution, however, has not been investigated at the genomic level. In this hypothesis and theory article, we provide preliminary evidence for positive selection in humans in the regions of two platforms of intragenomic conflict—chromosomes 15q11-q13 and X—and explore the potential relevance of cis-regulated imprinted domains to neocortical expansion in mammalian evolution. We present the hypothesis that maternal- and paternal-specific pressures on the developing neocortex compete intragenomically to influence neocortical expansion in mammalian evolution.