Constantine Argiris said... Actually, Orthodox priests do not shave their beards because Orthodox Christianity teaches us that vanity and the desire for physical perfection is a temptation by the devil designed to turn us away from God.onstantine Argiris said... Actually, Orthodox priests do not shave their beards because Orthodox Christianity teaches us that vanity and the desire for physical perfection is a temptation by the devil designed to turn us away from God.