For the selection of antioxidants, internal factors were proposed by analyzing the thermal-oxidative aging process, which consisted of the following two inseparable steps: (1) the physical process of oxygen (O) entering the rubber network and (2) the complex chemical process of O reacting with the rubber network. Antioxidants 2246, 6PPD, and MB, examples of amines, phenols, and heterocycles, respectively, were chosen to study these factors influencing the selection of antioxidants for the thermal-oxidative aging of butadiene rubber (BR). Through thermogravimetric analysis coupled with Fourier transform infrared spectroscopy and kinetic analysis by the Flynn-Wall-Ozawa method, the dissociation reaction of BR was identified to be the rate-determining step for the thermal-oxidative aging of BR. Meanwhile, the decisive positions of the dissociation reactions for the three antioxidants in improving the thermal-oxidative stability of BR were also identified. Therefore, the internal factors were subdivided into five items (i.e., the free energy of reaction for the dissociation of antioxidant, the mole ratio of active radicals or hydroperoxides that could react with the same mass of antioxidant, the solubility and mobility of the antioxidant in BR, and the permeability of O). Combined with molecular dynamics simulations and quantum mechanics simulations, the five internal factors were clarified and quantified over the entire usable temperature range of BR. To clarify the relative importance of each factor in the selection of antioxidants, we identified the time-dependent tensile strength and elongation at break as the only responses for the first and second gray relational analyses. The relative importance of the five internal factors was evaluated and ranked in terms of gray relational grade. The two analyses were consistent and showed that, in the selection of antioxidants, we should give priority to the free energy of the dissociation reaction and the permeability of O.