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Observations of the cold neutral atomic hydrogen (H i) in and around disc galaxies have revealed that spatial and kinematic asymmetries are common place, and are reflected in the global H i spectra. We use the TNG100 box from the IllustrisTNG suite of cosmological simulations to study the conditions under which these asymmetries may arise in current theoretical galaxy formation models. We find that more than 50 per cent of the sample has at least a 10 per cent difference in integrated flux between the high- and low-velocity half of the spectrum, thus the typical TNG100 galaxy has an H i profile that is not fully symmetric. We find that satellite galaxies are a more asymmetric population than centrals, consistent with observational results. Using halo mass as a proxy for environment, this trend appears to be driven by the satellite population within the virial radius of haloes more massive than 1013 M·, typical of medium/large groups. We show that, while the excess of H i asymmetry in group satellites is likely driven by ram pressure, the bulk of the asymmetric H i profiles observed in TNG100 are driven by physical processes able to affect both the central and satellite populations. Our results highlight how asymmetries are not driven solely by environment, and multiple physical processes can produce the same asymmetric shape in global H i spectra.