The unexpected bent geometries of some alkaline earth dihalides and dihydrides, ML2 (M = Ca, Sr, Ba; L = H, F, Cl, Br) have been explained in the literature using various models that attribute the effect to different phenomena like covalency, metal core polarization, sd-hybridization, and electron pair repulsion. We employ (based on first principles) the pseudo Jahn-Teller effect, as the only source of instability of high-symmetry configurations in nondegenerate states, to analyze the origin of the geometry of these systems and show that this approach explains all of their main structural features, including the topology of the Laplacian of the electron density and the vibrational frequencies. The main contribution to the distortion of the linear configuration is due to the pseudo Jahn-Teller mixing by bending of the sigma(u) HOMO formed by the ligand orbitals with the unoccupied pi(g) orbitals of the metal (with main d(xz) and d(yz) character), resulting in new covalency which stabilizes the bent configuration. We show that the model approaches to the problem, mentioned above, are either restricted particular cases of the pseudo Jahn-Teller interaction, or they yield very small contributions to the instability that do not explain the origin of the bending. All of our conclusions are supported by high-quality ab initio calculations.