We report on a first-principles study of the structural deformation modes in diamond, cubic boron nitride (c-BN), and cubic BC2N. We show that (i) the diamond C-C bonds remain strong up to the breaking point, leading to the large and nearly identical shear and tensile strength, (ii) c-BN exhibits a shear failure mode different from that in diamond and a significant softening in the B-N bonds at large tensile strains long before the bond breaking, and (iii) cubic BC2N displays a large disparity between the shear and tensile strength, contrary to the expectation for the hybrid of diamond and c-BN. We examine the microscopic bond-breaking processes to elucidate the atomistic mechanisms for the deformation modes and the implications for material strength.