Albert Barnes Commentary Exodus 19:4

"Ye have seen what I did unto the Egyptians, and how I bare you on eagles` wings, and brought you unto myself." — Exodus 19:4 (ASV)

On eagles’ wings - Both in the law (Deuteronomy 32:11) and in the Gospel (Matthew 23:37), the Church is compared to fledglings that the mother cherishes and protects under her wings.

In the law, however, that mother is an eagle, while in the Gospels she is “a hen.” This distinction foreshadows the diversity of administration under each covenant: the one of power, which God manifested when He brought His people out of Egypt with a mighty hand and an outstretched arm, and led them into the promised land; the other of grace, when Christ came in humility, took the form of a servant, and became obedient to death, even the death of the Cross.

Compare also Revelation 12:14.