The response of semiconductor materials to external magnetic fields is a reliable approach to probe intrinsic electronic and spin-dependent properties. In this study, we investigate the common Zeeman splitting features of novel wurtzite materials, namely, InP, InAs, and GaAs. We present values for the effective g factors of different energy bands and show that spin-orbit coupling effects, responsible for the spin splittings, also have noticeable contributions to the g factors. Within the Landau level picture, we show that the nonlinear Zeeman splitting recently explained in magnetophotoluminescence experiments for InP nanowires by D. Tedeschi et al. [Phys. Rev. B 99, 161204 (2019)] is also present in InAs, GaAs, and even the conventional GaN. Such nonlinear features stem from the peculiar coupling of the A and B valence bands as a consequence of the interplay between the wurtzite crystal symmetry and the breaking of time-reversal symmetry by the external magnetic field. Moreover, we develop an analytical model to describe the experimental nonlinear Zeeman splitting and apply it to InP and GaAs data. Extrapolating our fitted results, we found that the Zeeman splitting of InP reaches a maximum value, which is a prediction that could be probed at higher magnetic fields.