SnO₂ is an abundant, low cost, natively n-type, wide band gap oxide, which can achieve high conductivities due to facile donor doping. Realization of a p-type SnO₂ would, however, open up many new avenues in device applications, and has become a major research goal. Previous experimental and theoretical studies have proved inconclusive, with the p-type ability of SnO₂ being both supported and questioned in equal measure. In this study we use state of the art hybrid density functional theory to investigate the nature of intrinsic and extrinsic p-type defects in SnO₂. We demonstrate that all the p-type defects considered in SnO₂ produce localized hole polarons centered on anion sites. We calculate the thermodynamic ionization energies of these defects, and demonstrate that an efficient p-type SnO₂ is not achievable.