Using the first-principles approach, we investigated the electronic and chemical properties of wurtzite silicon carbide (2H-SiC) monolayer and thin film structures and substantiated their catalytic activity toward CO oxidation. 2H-SiC monolayer, being planar, is quite stable and has moderate binding with O2, while CO interacts physically; thus, the Eley-Rideal (ER) mechanism prevails over the Langmuir-Hinshelwood (LH) mechanism with an easily cleared activation barrier. Contrarily, 2H-SiC thin film, which exhibits a nonplanar structure, allows moderate binding of both CO and O2 on its surface, thus favoring the LH mechanism over the ER one. Comprehending these results leads to a better understanding of the reaction mechanisms involving structural contrast. Weak overlapping between the 2pz(C) and 3pz(Si) orbitals of the SiC monolayer system has been found to be the primary reason to revert the active site toward sp3 hybridization, during interaction with the molecules. In addition, the influences of graphite and Ag(111) substrates on the CO oxidation mechanism were also studied, and it is observed that the ER mechanism is preserved on SiC/G system, while CO oxidation on the SiC/Ag(111) system follows the LH mechanism. The calculated Sabatier activities of the SiC catalysts show that the catalysts are very efficient in catalyzing CO oxidation.