The training effect and asymmetry in exchange-coupled polycrystalline CoO/Co bilayers with in-plane magnetization has been investigated. This system is selected for its large training effect and initial asymmetry of the magnetic hysteresis after field cooling, which is removed after training. Applying an in-plane magnetic field perpendicular to the cooling field largely restores the untrained state with its pronounced asymmetry. The possibility to reinduce the asymmetry strongly depends on the magnitude of the perpendicular field, providing the key to identify the physical origin of training and removal of the asymmetry. These effects result from misalignment between the ferromagnetic magnetization and the uncompensated magnetization of the granular antiferromagnet.