The mechanical properties and electronic structure of recently synthesized PtN2, proposed as a potential candidate for superhard materials, have been investigated by means of density functional theory. Although it shows a clear band gap indicating a covalent bonding nature, the calculated shear moduli and ideal strengths of both proposed PtN2 polymorphs are much lower than those of ReB2, suggesting that it should be weaker than ReB2, whose load-invariant hardness is less than 30 GPa. The anisotropic strength of the pyrite PtN2 polymorph is significantly higher than that of the fluorite polymorph due to a larger covalent contribution. The shear instability for both polymorphs occurs in a cleavagelike mode between the weakly bonded crystal planes. This behavior is different from transition-metal (TM) diborides where the TM-TM or TM-B bonds are the carriers of the shear instability.