Zinc oxide can be reduced to metal by heating with carbon but $C{r}_2{O}_3$ cannot be reduced by heating with carbon, why?

Oxides of moderates reactive metals such as $Zn$ can be reduced by carbon because carbon has more affinity for oxygen than zinc due to which $ZnO$ is reduced to $Zn$ and carbon combines with oxygen to form $CO$. Whereas, oxides of chromium cannot be reduced by using carbon has less affinity for oxygen than chromium due to which chromium oxide is not reduced by carbon.