This paper constructs a Nuclear Shell Model composed of spin-coupled dinucleon nuclei. Using pn (proton-neutron) and nn (neutron-neutron) pairs formed by antiparallel spin coupling as the basic structural units of the atomic nucleus, a shell model isomorphic to the outer electron orbitals is established. By comparing the microscopic orbital configurations of various typical magic number nuclei, the formation of magic numbers is explained from the perspective of nuclear structure. This paper distinguishes between orbital shell configurations and the actual steady state of the atomic nucleus, thus resolving paradoxes that magic number models cannot explain, such as the instability of certain double magic number nuclei and the stability of isotopes in non-magic number nuclei. Research shows that a complete inner neutron cores is a necessary condition for maintaining the stable state of the atomic nucleus. Magic numbers merely represent the geometric characteristics of fully occupied orbitals and cannot be used as a standard for judging nuclear stability. This model can construct a unified nuclear shell system applicable to nuclei within the magic number range without the need for artificial fitting of empirical parameters, providing a new theoretical framework for studying nuclear structure and isotope stability.