Integral field galaxy surveys have discovered that galaxy spin (the relative contribution of rotation and random motion to dynamical support) depends on environment, galaxy mass and stellar population age. However, the key drivers have remained obscured. I will introduce the SAMI Galaxy Survey and use these data across a multi-dimensional parameter space to show that stellar population age is the dominant driver of galaxy spin. In fact, across our sample, once the relation between light-weighted age and spin is accounted for, there is no significant residual correlation between spin and mass, or spin and environment. This result is strongly suggestive that present-day environment only indirectly influences spin, via the removal of gas and star formation quenching. That is, environment affects age, then age affects spin. Older galaxies then have lower spin, either due to stars being born dynamically hotter (progenitor bias) at high redshift, or due to secular heating. The only regime in which environment plays a role in setting spin is for high-mass (log(M*)>11) galaxies, where there is a residual environmental trend with central galaxies preferentially having lower spin, compared to satellites of the same age and mass. We argue that this trend is likely due to central galaxies being a preferred location for mergers.