Recent measurements collected by the Mars Curiosity Rover at the Gale Crater revealed an unexpectedly large seasonal cycle of molecular oxygen (O2). We use a 1-D photochemical model, including inorganic and organic chemistry, and its adjoint model to quantify the sensitivity of changes in O2 to changes in inorganic and organic compounds. We show that O2 changes are most sensitive to changes in organic compounds from the oxidation of methane. We find that an accelerated loss of atmospheric methane, achieved either by increasing the atmospheric loss or by imposing an additional surface loss, does not reconcile model and observed values of O2 but it helps to explain the O2 seasonal variation. The resulting changes in atmospheric composition are below the detection limits of orbiting instruments.