The offset of high redshift star-forming galaxies in the [OIII]/H$beta$ versus [NII]/H$alpha$ (O3N2) diagram in comparison with the local star-forming galaxy sequence is now well established. The physical origin of the shift is the subject of some debate, and has important implications for metallicity measurements based on strong lines at all redshifts. To investigate the origin of the O3N2 offset, we use a sample of ~100,000 star-forming galaxies from SDSS DR12 to probe the empirical correlations between emission line diagnostics and measurable galaxy physical properties. In particular, we examine how surface density of star formation, ionization parameter, nitrogen-to-oxygen (N/O) ratio, and stellar mass drive position in two key diagnostic diagrams: O3N2 and [OIII]/H$beta$ versus [SII]/H$alpha$ (O3S2). We show that, at fixed [OIII]/H$beta$, galaxies falling closer to the high-redshift locus in O3N2 have higher star formation density, stellar mass and N/O ratios. We also find a tight correspondence in the distributions of stellar mass and N/O in the diagnostic diagrams. This relation, spanning a range of galaxy evolutionary states, suggests that the N/O-$M_{*}$ relation is more fundamental than the N/O-metallicity relation. We argue that a tight N/O-$M_{*}$ relation is well-motivated physically, and that the observed correlation of N/O with O/H in the local universe is primarily a reflection of the existence of the mass-metallicity relation. Because the mass-metallicity relation evolves much more rapidly with redshift than N/O-$M_{*}$, the N/O ratios of high redshift galaxies are significantly elevated in comparison with local galaxies with the same gas-phase O/H. The O3N2 shift and elevated N/O ratios observed in high redshift galaxies therefore come about as a natural consequence of the N/O-$M_{*}$ relation combined with the evolution of the mass-metallicity relation.
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