We present unprecedented results on the damage thresholds and pathways for boron nitride nanotubes (BNNT) under the influence of energetic electrons in an oxidative gas environment, using an environmental aberration-corrected electron microscope over a range of oxygen pressures. We observe a damage cascade process that resists damage until a higher electron dose, compared with carbon nanotubes, initiating at defect-free BNNT sidewalls and proceeding through the conversion from crystalline nanotubes to amorphous boron nitride (BN), resisting oxidation throughout. We compare with prior results on the oxidation of carbon nanotubes and present a model that attributes the onset of damage in both cases to a physisorbed oxygen layer that reduces the threshold for damage onset. Surprisingly, increased temperatures offer protection against damage, as do electron dose rates that significantly exceed the oxygen dose rates, and our model attributes both effects to a physisorbed oxygen population.