ALMA observations of $z>6$ galaxies have revealed abnormally high [OIII]$_{\rm 88\mu m}$/[CII]$_{\rm 158\mu m}$ ratios and [CII]$_{\rm 158\mu m}$ deficits compared to local galaxies. Numerous solutions have been proposed including differences in C and O abundance ratios, observational bias, and differences in ISM properties. In order to elucidate the underlying physics that drives this high-redshift phenomenon, we employ SPHINX$^{20}$, a state-of-the-art, cosmological radiation-hydrodynamics simulation, that resolves detailed ISM properties of thousands of galaxies in the epoch of reionization. We find that the observed $z>6$ [OIII]-SFR and [CII]-SFR relations can only be reproduced when the C/O abundance ratio is $\sim8\times$ lower than Solar and the total metal production is $\sim4\times$ higher than that of a Kroupa IMF. This implies that high-redshift galaxies are potentially primarily enriched by low-metallicity core-collapse supernovae with a more top-heavy IMF. As AGB stars and type-Ia supernova begin to contribute to the galaxy metallicity, both the [CII]-SFR and [CII] luminosity functions are predicted to converge to observed values at $z\sim4.5$. While we demonstrate that ionisation parameter, LyC escape fraction, ISM gas density, and CMB attenuation all drive galaxies towards higher [OIII]/[CII], observed values at $z>6$ can only be reproduced with substantially lower C/O abundances compared to Solar. The combination of [CII] and [OIII] can be used to predict the values of ionisation parameter, ISM gas density, and LyC escape fraction and we provide estimates of these quantities for nine observed $z>6$ galaxies. Finally, we demonstrate that [OI]$_{\rm 63\mu m}$ can be used as a replacement for [CII] in high-redshift galaxies where [CII] is unobserved and argue that more observation time should be used to target [OI] at $z>6$. (Abridged)