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The Baldwin, Philips, & Terlevich diagram of [O III]/H$β$ vs. [N II]/H$α$ (hereafter N2-BPT) has long been used as a tool for classifying galaxies based on the dominant source of ionizing radiation. Recent observations have demonstrated that galaxies at $z\sim2$ reside offset from local galaxies in the N2-BPT space. In this paper, we conduct a series of controlled numerical experiments to understand the potential physical processes driving this offset. We model nebular line emission in a large sample of galaxies, taken from the SIMBA cosmological hydrodynamic galaxy formation simulation, using the CLOUDY photoionization code to compute the nebular line luminosities from H II regions. We find that the observed shift toward higher [O III]/H$β$ and [N II]/H$α$ values at high redshift arises from sample selection: when we consider only the most massive galaxies $M_* \sim 10^{10-11} M_\odot$, the offset naturally appears, due to their high metallicities. We predict that deeper observations that probe lower-mass galaxies will reveal galaxies that lie on a locus comparable to $z\sim 0$ observations. Even when accounting for sample selection effects, we find that there is a subtle mismatch between simulations and observations. To resolve this discrepancy, we investigate the impact of varying ionization parameters, H II region densities, gas-phase abundance patterns, and increasing radiation field hardness on N2-BPT diagrams. We find that either decreasing the ionization parameter or increasing the N/O ratio of galaxies at fixed O/H can move galaxies along a self-similar arc in N2-BPT space that is occupied by high-redshift galaxies.