The elastic modulus of metallic glasses (MGs) is commonly considered to be “inherited” from their solvent (principal) element. However, this rule exhibits significant exceptions in Cu-based MG systems. To uncover the physical mechanism behind this anomalous inheritance, this study selected the Cu-Zr-Hf-Ti system as the research object. Based on first-principles calculations, a multi-scale analysis was conducted, including the macroscopic elastic modulus, atomic-scale bonding characteristics, and the electronic structure. The results show that the elastic modulus of this system is governed by low-stiffness interatomic interactions represented by Zr-Zr and Zr-Ti bonds, rather than by the principal element Cu. Electronic structure analysis further confirms that, although Cu dominates in composition, the electronic density of states (DOS) near the Fermi level is primarily contributed by the d-orbitals of the minor elements Zr and Hf. The introduction of Hf enhances the orbital hybridization between Cu-3d and Hf-5d, and reduces DOS near the Fermi level, thereby significantly increasing stiffness by promoting the directionality and covalency of bonding. Concurrently, the decrease in ratio of bulk modulus to shear modulus (B/G) and Poisson's ratio (ν) values suggests a potential decline in toughness. This work clarifies that the inheritance of the elastic modulus in MGs is essentially determined by the key element that dominates the electronic DOS at the Fermi level. This finding provides a theoretical basis for the rational design of MGs with tailored mechanical properties from an electronic structure perspective.