Water is known to be an exceptionally poor glass former, which is a significant drawback in the low-temperature storage of food and biomatter. This is one of the characteristic features of water, but its link to the thermodynamic and kinetic anomalies of water remains elusive. Recently, we showed that the glass-forming ability and the fragility of a water/salt mixture are closely related to its equilibrium phase diagram [Kobayashi, M.; Tanaka, H. Phys. Rev. Lett. 2011, 106, 125703]. Here we propose that frustration between local and global orderings controls both "the glass-forming ability and fragility on the basis of experimental evidence. Relying on the same role of salt and pressure, which commonly breaks tetrahedral order, we apply this idea to pure water under pressure. This scenario not only explains unusual behavior of water-type liquids such as water, Si, and Ge but also provides a general explanation on the link between the equilibrium phase diagram, the glass-forming ability, and the fragility of various materials including oxides, chalcogenides, and metallic glasses.