Electrides are unique materials in which electrons occupy interstitial regions formed by cation frameworks and act as anions. They have many interesting properties and are often induced by high pressure in some materials. Understanding the emergence of electride states is a central problem in condensed-matter physics. While existing theoretical frameworks, including the interstitial quasi-atom (ISQ) and electron-ion interaction (EII) models, have provided some useful phenomenological interpretations of the electride formation, the atomistic origin and the underlying physics of this charge redistribution remain unclear. Here, within a first-principles framework, we systematically study the evolution of electronic structures of compressed materials, using alkali metals as representative examples. By mapping symmetry-resolved electronic band states onto atomic orbitals, we find that (i) pressure-induced quantum confinement raises the energies of atomic orbitals due to enhanced kinetic energy and increased overlap between valence and core electrons, with the energy shift being larger for more delocalized s orbital than for more localized p and d orbitals; and (ii) this effect causes reordering of band states, making the electride states, which are composed of the interatomic hybridized pd orbitals, to progressively shift in energy below the s orbital states, leading to their occupation and the onset of electride behavior. This microscopic electronic-state picture clarifies the origin of the electride formation and provides a general framework for understanding the evolution of interstitial electronic states under compression across diverse materials.