The Buddha explains how his teaching of the Dhamma inspires fear and dread in the deities, just as the lion's roar inspires fear in the animals.

Sīha sutta - The Lion

At Sāvatthī.

"Bhikkhus, the lion, the king of animals, in the evening time, leaves his lair; having left his lair, he stretches; having stretched, he looks around in all four directions; having looked around in all four directions, he roars his lion's roar three times; having roared his lion's roar three times, he departs to search for food. When the lion, the king of animals, roars, whatever animals hear the sound of his roar are for the most part filled with fear, a sense of urgency, and dread. Those who live in the holes enter their holes; those who live in the water enter the water; those who live in the forest enter the forest; and the birds flee to the sky. Even those royal elephants, bhikkhus, that are bound with strong ropes in the villages, market towns, and royal capitals, they too, having broken and smashed those bonds, afraid, excreting dung and urine, flee here and there. Thus, bhikkhus, the lion, the king of animals, among the animals, is indeed possessed of great power, influence, and majesty.

In the same way, bhikkhus, when the Tathāgata arises in the world, the Arahant, perfectly enlightened, accomplished in wisdom and conduct, well-gone, knower of the world, the unsurpassed leader of persons to be trained, the teacher of gods and humans, the Buddha, the Blessed One, he teaches the Dhamma thus: 'Such is form, such is the arising of form, such is the dissolution of form; such is feeling, such is the arising of feeling, such is the dissolution of feeling; such is perception, such is the arising of perception, such is the dissolution of perception; such are formations, such is the arising of formations, such is the dissolution of formations; such is consciousness, such is the arising of consciousness, such is the dissolution of consciousness.'

Even those deities, bhikkhus, who are long-lived, possessed of beauty, abundant in happiness, dwelling in high celestial mansions for a long time, they too, having heard the Tathāgata's teaching of the Dhamma, are for the most part filled with fear, a sense of urgency, and dread: "It seems, sir, that we are unstable, though we thought ourselves to be stable; it seems, sir, that we are not enduring, though we thought ourselves to be enduring; it seems, sir, that we are not everlasting, though we thought ourselves to be everlasting. It seems, sir, that we are unstable, not enduring, not everlasting, embodied in an individual identity. Thus, bhikkhus, the Tathāgata is indeed possessed of great power, influence, and majesty over the world with its gods."

The Blessed One spoke this. Those bhikkhus were satisfied and rejoiced in the Blessed One's words. The Teacher said this:

"When the Buddha, having directly realized, sets in motion the wheel of Dhamma; For the world with its gods, he is the peerless teacher.
He taught the cessation of self-identity, and the arising of self-identity; And the Noble Eightfold path, leading to the alleviation of suffering.
Then even those long-lived deities, possessed of beauty and celebrated; Are filled with fear, and dread, like animals before the lion's roar.
'We've not transcended self-identity, It seems, sir, we're not stable;' Thus they say, having heard the words of the Arahant, the steadfast, fully liberated one."