ABSTRACT We study the shapes of spatially integrated $\rm{H}\, \small {{I}}$ emission-line profiles of galaxies in the eagle simulation using three separate measures of the profile’s asymmetry. We show that the subset of eagle galaxies whose gas fractions and stellar masses are consistent with those in the xGASS survey also have similar $\rm{H}\, \small {{I}}$ line asymmetries. Central galaxies with symmetric $\rm{H}\, \small {{I}}$ line profiles typically correspond to rotationally supported $\rm{H}\, \small {{I}}$ and stellar discs, but those with asymmetric line profiles may or may not correspond to dispersion-dominated systems. Galaxies with symmetric $\rm{H}\, \small {{I}}$ emission lines are, on average, more gas rich than those with asymmetric lines, and also exhibit systematic differences in their specific star formation rates, suggesting that turbulence generated by stellar or AGN feedback may be one factor contributing to $\rm{H}\, \small {{I}}$ line asymmetry. The line asymmetry also correlates strongly with the dynamical state of a galaxy’s host dark matter halo: older, more relaxed haloes host more-symmetric galaxies than those hosted by unrelaxed ones. At fixed halo mass, asymmetric centrals tend to be surrounded by a larger number of massive subhaloes than their symmetric counterparts, and also experience higher rates of gas accretion and outflow. At fixed stellar mass, central galaxies have, on average, more symmetric $\rm{H}\, \small {{I}}$ emission lines than satellites; for the latter, ram pressure and tidal stripping are significant sources of asymmetry.