From The Gospel of Matthew, by Curtis Mitch and Edward Sri, commenting on Matthew 3:13-17
The Spirit descending like a dove recalls Noah’s dove that signaled the end of the flood and the beginning of the new world (Gen 8:8–12). It also recalls the Spirit of God over the waters of creation in Gen 1:2, where the Hebrew text describes the Spirit as “hovering” or “fluttering” over the waters like a bird. With these images from Genesis in the background, Matthew suggests that this event at the beginning of Jesus’ public ministry—his ministry whereby he will redeem humanity—marks the beginning of a new world, a new creation….
St. Cyril of Jerusalem reflects the Patristic tradition of seeing the story of Noah and the flood as prefiguring Jesus and his baptism. As the dove of Noah’s ark signified the renewed peace between God and man, so the dove descending on Christ points to the reconciliation he will bring about between God and all humanity.
“Just as salvation came in the time of Noah by the wood and the water, and there was the beginning of a new creation, and as the dove came back to Noah in the evening with an olive branch, so, they say, the Holy Spirit came down on the true Noah, the Author of the new creation, when the spiritual dove came down upon Him at His baptism to show that He is the One Who, by the wood of the cross, confers salvation on believers, and Who, toward the evening, by His death, gave the world the grace of salvation.”