Gloucester is too easily swayed by one son against the other. He is quick to believe the worst of Edgar, based on Edmund's lies. The foundation of favoritism that has existed in their relationship exposed Gloucester's insecurities, thus making it not at all difficult for Edmund to convince him of Edgar's perfidy.
Without the trust in his son's judgment, Gloucester rejects Edgar out of hand. He is influenced by appearance and strength of personaility, rather than on past experience of Edgar's loyalty and love. This mirrors Lear's rejection of Cordelia.