ABSTRACT We develop a 2D inclined rotating disc model, which we apply to the stellar velocity maps of 1862 galaxies taken from the MaNGA survey (SDSS public Data Release 15) . We use a random forest classifier to identify the kinematic parameters that are most connected to galaxy quenching. We find that kinematic parameters that relate predominantly to the disc (such as the mean rotational velocity) and parameters that characterize whether a galaxy is rotation- or dispersion-dominated (such as the ratio of rotational velocity to velocity dispersion) are not fundamentally linked to the quenching of star formation. Instead, we find overwhelmingly that it is the absolute level of velocity dispersion (a property that relates primarily to a galaxy’s bulge/spheroidal component) that is most important for separating star-forming and quenched galaxies. Furthermore, a partial correlation analysis shows that many commonly discussed correlations between galaxy properties and quenching are spurious, and that the fundamental correlation is between quenching and velocity dispersion. In particular, we find that at fixed velocity dispersion, there is only a very weak dependence of quenching on the disc properties, whereby more discy galaxies are slightly more likely to be forming stars. By invoking the tight relationship between black hole mass and velocity dispersion, and noting that black hole mass traces the total energy released by active galactic nuclei (AGNs), we argue that these data support a scenario in which quenching occurs by preventive feedback from AGNs. The kinematic measurements from this work are publicly available.