Recently, numerous methods for measuring [Fe/H] in M dwarf stars have been published. Some methods now claim <0.1 dex precision despite the fact that they do not directly probe Fe abundance. We present an investigation of NIR synthetic M dwarf spectra based on PHOENIX stellar atmosphere models to explore the effects of C and O abundances on M dwarf metallicity indicators. We find that the pseudo-continuum level is very sensitive to C/O and that all metallicity indicators investigated show a dependence on C and O abundances, especially at lower Teff. In some cases the inferred metallicity ranges over a full order of magnitude (>1 dex) when [C/Fe] and [O/Fe] are varied independently by +/-0.2. Models of mid-M dwarfs with [C/Fe], [O/Fe], and [M/H] that are realistic in the context of galactic chemical evolution suggest variations in C and O abundances are the primary physical mechanism behind M dwarf metallicity tracers that are based on the equivalents widths of metal lines in moderate-resolution NIR spectra. We suggest that mid-M dwarf metallicity calibrations are a product of the tight correlation between C/O and [Fe/H], a trend confirmed by spectroscopic surveys of solar neighborhood FGK stars. Variations in C and O abundances also affect the spectral energy distribution of M dwarfs. Allowing C/O to be a free parameter provides better agreement between synthetic spectra and observed spectra of metal-rich M dwarfs. We suggest that flux-calibrated, low-resolution, NIR spectra can provide a path toward measuring C and O abundances in M dwarfs and breaking the degeneracy between C/O and [Fe/H] present in M dwarf metallicity indicators.