The ilmenite-type MgMnO3 and ZnMnO3 with honeycomb Mn layers exhibit distinctive magnetic ground states. In experiments, MgMnO3 exhibits a Neel antiferromagnetic alignment, in which both nearest-neighbor (NN) J(1) and next-nearest-neighbor (NNN) J(2) exchange interactions are antiferromagnetic, while ZnMnO3 has zigzag antiferromagnetic ordering with NN ferromagnetic and NNN antiferromagnetic coupling. On the basis of ab initio band structure calculations, we explain the deviation of NN J(1) exchange coupling from antiferromagnetic (MgMnO3) to ferromagnetic (ZnMnO3) as originating from the intensive hybridization between the occupied Zn 3d(10) orbitals with those of the bridging O 2p states, strongly depending on the position of the orbitals. In addition, our results indicate that, in combination with the NN J(1) coupling, the considerably large third-nearest-neighbor (TNN) J(3) exchange interaction plays an important role in erecting the magnetic ground states, rather than the experimentally proposed NNN J(2). Furthermore, our findings highlight the important role of not only the electronic configurations but also the positions of the nonmagnetic cations in determining the essence of the magnetic exchange interactions. Therefore, the hybridization effect of nonmagnetic cations should not be dismissed in an analysis of the magnetic properties of transition-metal oxides.