A phenomenon appears in a few examples of the chalcopyrites (space group I-42 d) where heavier atoms do not necessarily lead to lower lattice thermal conductivity, in contradiction with Keyes expression that formulates an inverse relation of thermal conductivity with mean atomic mass. Herewith, the thermal conductivity of CuInSe2, CuInTe2, AgInSe2, and AgInTe2 was calculated and compared at room temperature from the linearized Boltzmann transport equation using ab initio density functional theory. CuInSe2 and AgInSe2 solids exhibit lower lattice thermal conductivity than that of CuInTe2 and AgInTe2, respectively, despite the fact that Te atoms are significantly heavier than Se. A comparison between dispersion relation, the Grüneisen parameter, and projected density of states leads to the conclusion that anharmonic transverse acoustic modes in the form of anomalous vibrations of Cu and Ag cause the lower values of the thermal conductivity. By analyzing the electronic structure, the compounds under study fit perfectly into a recently defined region of the metavalent bonding well known for its pronounced anharmonicity. The insight gained from the current results deepens our understanding of the unusual heat transfer phenomenon related to the metavalent bonding and sheds light on design and discovery of thermally functional materials that break the prediction by the conventional theory.