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Though YB6 and LaB6 share the same crystal structure, atomic valence electron configuration, and phonon modes, they exhibit drastically different phonon-mediated superconductivity. YB6 superconducts below 8.4 K, giving it the second-highest critical temperature of known borides. LaB6 does not superconduct until near-absolute zero temperatures, however. Though previous studies have quantified the canonical superconductivity descriptors of YB6’s greater Fermi-level (Ef) density of states and higher electron-phonon coupling (EPC), the root of this difference has not been assessed with full detail of the electronic structure. Through chemical bonding, we determine low-lying, unoccupied 4f atomic orbitals in lanthanum to be the key difference between these superconductors. These orbitals, which are not accessible in YB6, hybridize with pi B-B bonds and bring this pi-system lower in energy than the sigma B-B bonds otherwise at Ef. This inversion of bands is crucial: the phonon modes we show responsible for superconductivity cause the sigma-orbitals of YB6 to change drastically in overlap, but couple weakly to the pi-orbitals of LaB6. These phonons in YB6 even access an electronic-state crossing, indicating strong EPC. No such crossing in LaB6 is observed. Finally, a supercell (the M k-point) is shown to undergo a Peierls-like effect in YB6, introducing additional EPC. Use of Quantum Espresso's EPC functionality for determination of the relevant modes and supercells, coupled to the electronic structure of these two borides, is discussed.