The Screech Owl is the sacred bird of Hades because it was his way of showing honor to Askalaphus. Askalaphus was a servant of Hades who had testified that Persephone had eaten some of the food of the dead and as such Persephone was forced to spend time in the Underworld. Demeter let loose her wrath the first time by burying Asklaphus under a boulder
Centuries after being trapped under the boulder, Herakles performing his twelfth labor went to the underworld and came across Askalaphus buried under the stone. As Herakles had great strength he was able to remove the stone freeing Askalaphus. Demeter learned that Askalaphus had been freed and while she did not begrudge Herakles for liberating Askalaphus she had not and would never forgive. As such Demeter transformed Askalaphus into a Screech Owl. Unlike Demeter, Hades viewed Askalaphus as a loyal servant who had twice been punished by Demeter for his loyalty to the Lord of the Underworld. Though it was not within Hades power to transform Askalaphus back he compensated him by making the Screech Owl a sacred animal.