A well-known feature of the -based superconductors is the pressure-induced collapsed tetragonal phase that is commonly ascribed to the formation of an interlayer As–As bond. Using detailed x-ray scattering and spectroscopy, we find that Rh-doped does not undergo a first-order phase transition and that local Fe moments persist despite the formation of interlayer As–As bonds. Our density functional theory calculations reveal that the Fe–As bond geometry is critical for stabilizing magnetism and the pressure-induced drop in the lattice parameter observed in pure is mostly due to a constriction within the FeAs planes. The collapsed tetragonal phase emerges when covalent bonding of strongly hybridized Fe and As states completely wins out over their exchange splitting. Thus the collapsed tetragonal phase is properly understood as a strong covalent phase that is fully nonmagnetic with the As–As bond forming as a by-product.