We investigate the microscopic origin of water's anomalies by inspecting the hydrogen bond network (HBN) and the spatial organization of low-density-liquid (LDL) like and high-density-liquid (HDL) like environments. Specifically, we simulate - via classical molecular dynamics simulations - the isobaric cooling of a sample composed of 512 water molecules from ambient to deeply undercooled conditions at three pressures, namely, 1 bar, 400 bars, and 1000 bars. In correspondence with the Widom line (WL), (i) the HDL-like dominating cluster undergoes fragmentation caused by the percolation of LDL-like aggregates following a spinodal-like kinetics; (ii) such fragmentation always occurs at a "critical" concentration of ∼20%-30% in LDL; (iii) the HBN within LDL-like environments is characterized by an equal number of pentagonal and hexagonal rings that create a state of maximal frustration between a configuration that promotes crystallization (hexagonal ring) and a configuration that hinders it (pentagonal ring); (iv) the spatial organization of HDL-like environments shows a marked variation. Moreover, the inspection of the global symmetry shows that the intermediate-range order decreases in correspondence with the WL and such a decrease becomes more pronounced upon increasing the pressure, hence supporting the hypothesis of a liquid-liquid critical point. Our results reveal and rationalize the complex microscopic origin of water's anomalies as the cooperative effect of several factors acting synergistically. Beyond implications for water, our findings may be extended to other materials displaying anomalous behaviours.