Hexagonal boron nitride (h-BN), known for its exceptional thermal and chemical stability, is widely used in high-temperature applications and as an encapsulation layer for other twodimensional materials. This study examines the dissociation mechanisms of O2 molecules on the h-BN surface, focusing on activation energies and minimum energy pathways at different adsorption sites using climbing-image nudged elastic band (CI-NEB) calculations. The results reveal several dissociation pathways with significant variations in activation barriers depending on site and configuration, including one low-barrier route favorable for surface reactions. Reactive molecular dynamics (RMD) simulations with the ReaxFF force field are employed to investigate oxidation behavior in multilayer h-BN at 900 K, 1200 K, and 1500 K. At 900 K, O2 adsorbs without penetrating beneath the surface, while higher temperatures enhance dissociation and promote deeper oxygen incorporation. Charge analysis at elevated temperatures shows stronger chemisorption and electron transfer, forming a more uniform, chemically bonded oxygen layer.