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Deformation and fracture of metallic glasses are often modeled by stress-based criteria which often incorporate some sorts of pressure dependence. However, detailed mechanisms that are responsible for the shear-band formation and the entire damage initiation and evolution process are complex and the origin of such a pressure dependence is obscure. Here, we argue that the shear-band formation results from the constitutive instability, so that the shear-band angle and arrangements can be easily related to the macroscopic constitutive parameters such as internal friction and dilatancy factor. This is one reason for the observed tension-compression asymmetry in metallic glasses. The free volume coalescence leads to precipitous formation of voids or cavities inside the shear bands, and the intrinsic “ductility” is therefore governed by the growth of these cavities. Based on a generalized Stokes–Hookean analogy, we can derive the critical shear-band failure strain with respect to the applied stress triaxiality, in which the cavity evolution scenarios are sharply different between tension-controlled and shear/compression-dominated conditions. This is another possible reason for the tension-compression asymmetry. It is noted that diffusive-controlled cavity growth could also be the rate-determining process, as suggested by the recent measurements of shear-band diffusivity and viscosity that turn out to satisfy the Stokes–Einstein relationship. This constitutes the third possible reason for the tension-compression asymmetry.