The metal-support interaction is one of the most important pillars in heterogeneous catalysis, but developing a fundamental theory has been challenging because of the intricate interfaces. Based on experimental ‎data, interpretable machine learning, theoretical derivation, and first-principles simulations, we established a ‎general theory of metal-oxide interactions grounded in ‎metal-metal and metal-oxygen interactions. The theory applies to metal nanoparticles and atoms on oxide supports and oxide films on metal supports. We found that for late-transition metal catalysts, metal-metal interactions dominated the oxide support effects and suboxide encapsulation over metal nanoparticles. A principle of strong metal-metal interactions for encapsulation occurrence is formulated and substantiated by extensive ‎experiments including 10 metals and 16 ‎oxides. The valuable insights revealed on (strong) metal-support interaction advance the interfacial design of supported metal catalysts.