When electric and magnetic fields are applied together on a magnetoelectric antiferromagnet, the domain state is subject to reversal. Although the initial and final conditions are saturated singledomain states, the process of reversal may decompose into local multi-domain switching events. In thin films of Cr2O3, the magnetoelectric coercivity and the switching speed found from experiments are considerably lower than expected from magnetic anisotropy, similar to Brown's paradox in ferromagnetic materials. Multi-domain effects originate because antiferromagnetic domain walls are metastably pinned by lattice defects, not due to reduction of magnetostatic energy, which is negligible. This paper theoretically analyzes domain reversal in thin-film magnetoelectric antiferromagnets in the form of nucleation, domain wall propagation, and coherent rotation. The timescales of reversal mechanisms are modeled as a function of applied magnetoelectric pressure. The theory is assessed with reference to latest experimental works on magnetoelectric switching of thin-film Cr2O3: domain wall propagation is found to be dominant and responsible for switching in the experiments. The results bear implications in the energy-delay performance of ME memory devices utilizing antiferromagnetic insulators, which are prospective for nonvolatile technology.