Silicon carbide (SiC) is an attractive semiconductor material for applications in power electronic devices. However, fabrication of a high-quality SiC/SiO2 interface has been a challenge. It is well-known that there is a great difference in the oxidation rate between the Si-face and the C-face and that the quality of oxide on the Si-face is greater than that on the C-face. However, the atomistic mechanism of the thermal oxidation of SiC remains to be solved. In this paper, a new Si-O-C interatomic potential was developed to reproduce the kinetics of the thermal oxidation of SiC. Using this newly developed potential, large-scale SiC oxidation simulations at various temperatures were performed. The results showed that the activation energy of the Si-face is much larger than that of the C-face. In the case of the Si-face, a flat and aligned interface structure including Si1+ was created. Based on the estimated activation energies of the intermediate oxide states, it is proposed that the stability of the flat interface structure is the origin of the high activation energy of the oxidation of the Si-face. In contrast, in the case of the C-face, it is found that the Si atom at the interface is easily pulled up by the O atoms. This process generates the disordered interface and decreases the activation energy of the oxidation. It is also proposed that many excess C atoms are created in the case of the C-face.