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ZnO typifies a class of materials that can be doped via native defects in only one way: either n type or p type. We explain this asymmetry in ZnO via a study of its intrinsic defect physics, including ${\mathrm{Zn}}_{\mathrm{O}},$ ${\mathrm{Zn}}_{i},$ ${\mathrm{V}}_{\mathrm{O}},$ ${\mathrm{O}}_{i},$ and ${V}_{\mathrm{Zn}}$ and n-type impurity dopants, Al and F. We find that ZnO is n type at Zn-rich conditions. This is because (i) the Zn interstitial, ${\mathrm{Zn}}_{i},$ is a shallow donor, supplying electrons; (ii) its formation enthalpy is low for both Zn-rich and O-rich conditions, so this defect is abundant; and (iii) the native defects that could compensate the n-type doping effect of ${\mathrm{Zn}}_{i}$ (interstitial O, ${\mathrm{O}}_{i},$ and Zn vacancy, ${V}_{\mathrm{Zn}}),$ have high formation enthalpies for Zn-rich conditions, so these ``electron killers'' are not abundant. We find that ZnO cannot be doped p type via native defects $({\mathrm{O}}_{i},{V}_{\mathrm{Zn}})$ despite the fact that they are shallow (i.e., supplying holes at room temperature). This is because at both Zn-rich and O-rich conditions, the defects that could compensate p-type doping ${(V}_{\mathrm{O}}{,\mathrm{}\mathrm{Zn}}_{i},{\mathrm{Zn}}_{\mathrm{O}})$ have low formation enthalpies so these ``hole killers'' form readily. Furthermore, we identify electron-hole radiative recombination at the ${V}_{\mathrm{O}}$ center as the source of the green luminescence. In contrast, a large structural relaxation of the same center upon double hole capture leads to slow electron-hole recombination (either radiative or nonradiative) responsible for the slow decay of photoconductivity.