  A well-known feature of CaFe$_{2}$As$_{2}$-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 Ca$_{0.8}$Sr$_{0.2}$Fe$_{2}$As$_{2}$ 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 that the pressure-induced drop in the $c$ lattice parameter
observed in pure CaFe$_{2}$As$_{2}$ is mostly due to a constriction within the
FeAs planes. These phenomena are best understood using an often overlooked
explanation for the equilibrium Fe-As bond geometry, which is set by a
competition between covalent bonding and exchange splitting between strongly
hybridized Fe $3d$ and As $4p$ states. In this framework, the collapsed
tetragonal phase emerges when covalent bonding completely wins out over
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 byproduct.
