Using first-principles density-functional theory calculations, an in-depth study on the divalent 3d transition-metal carbodiimides with the general formula MNCN (M = Cr-Cu) is performed. Experimentally, two different types of crystal structures are adopted for these, namely the (Jahn-Teller distorted) nickel arsenide [NiAs] and the rock salt [NaCl] type, and their occurrence from the formation energy and chemical bonding is rationalized. As already suspected many years ago, on the basis of empirical tight-binding arguments, the intrinsic mechanism for the preferred crystal structure lies in the metal-metal overlap population, reflected from crystal orbital Hamilton population (COHP) analysis data. Not too surprisingly, there is an increase in covalency for the metal-N bonds in MNCN upon increasing the atomic number of the metal, well-mirrored in the COHP, Mulliken charge transfer, and also charge-density analysis.