Emission lines with a double-peak (DP) shape, detected in the centre of galaxies, have been extensively used in the past to identify peculiar kinematics such as dual active galactic nuclei (AGNs), outflows, or mergers. With a more general approach considering a large DP galaxy sample selected from the Sloan Digital Sky Survey (SDSS), a connection to minor merger galaxies with ongoing star formation was suggested. To gain a better understanding of different mechanisms creating a DP signature, in this paper, we explore synthetic SDSS spectroscopic observations computed from disc models and simulations. We show how a DP signature is connected to the central part of the rotation curve of galaxies, which is mostly shaped by the stellar bulge. We, furthermore, find that bars can create strong DP emission-line signatures when viewed along their major axis. Major mergers can form a central rotating disc in late post-coalescence merger stages (1 Gyr after the final coalescence), which creates a DP signature. Minor mergers tend to show a DP feature with no correlation to the galaxy inclination within 350 Myr after the final coalescence. Comparisons of these scenarii with observations disfavour major mergers, since they show predominantly elliptical and only a few S0 morphologies. Furthermore, at such a late merger stage, the enhanced star formation is most likely faded. Bars and minor mergers, on the other hand, can be compared quite well with the observations. Both observations coincide with increased star formation found in observations, and minor mergers in particular do not show any dependency with the observation direction. However, observations resolving the galaxy kinematics spatially are needed to distinguish between the discussed possibilities. More insight into the origin of DP will be gained by a broader comparison with cosmological simulations. The understanding of the DP origin can provide important tools to study the mass growth of galaxies in future high redshift surveys.