And it came to pass that when all the people were baptized, Jesus also was baptized, and prayed (Luke 3:21).
Was He too then in need of holy baptism? But what benefit could accrue to Him from it?
The Only-begotten Word of God is Holy of the Holy: so the Seraphim name Him in their praises.
[...] “There is one Lord Jesus Christ,” as it is written….
He [i.e. Christ in His humanity] was not separate from Him [the Word], and by Himself when baptized and made partaker of the Holy Ghost.
For we know, both that He is God, and without stain, and Holy of the Holy. For we confess that “of His fulness have all we received.”
For the Holy Spirit indeed proceeds from God the Father, but belongs also to the Son.
It is even often called the Spirit of Christ, though proceeding from God the Father.
And to this Paul will testify, saying, at one time, “They that are in the flesh cannot please God: but ye are not in the flesh, but in the spirit, if so be the Spirit of God dwells in you. But if any one have not the Spirit of Christ, he is none of His.”
And again, “But because ye are sons, God hath sent the Spirit of His Son into your hearts, crying, Father, our Father.”
The Holy Spirit therefore proceeds indeed as I said from God the Father, but His Only-begotten Word, as being both by nature and verily Son, and resplendent with the Father’s dignities, ministers It to the creation, and bestows It on those that are worthy.
Truly He said, “All things that the Father hath are mine.” … But how then…was He baptized, and received also the Spirit?
[...] He had no need of holy baptism, being wholly pure and spotless, and holy of the holy. Nor had He need of the Holy Ghost: for the Spirit That proceeds from God the Father is of Him, and equal to Him in substance.
We must now therefore at length hear what is the explanation of the economy. God in his love to man provided for us a way of salvation and of life.
For believing in the Father, Son, and Holy Ghost, and making this confession before many witnesses, we wash away all the filth of sin, and are enriched by the communication of the Holy Spirit, and made partakers of the divine nature, and gain the grace of adoption.
It was necessary therefore that the Word of the Father, when He humbled Himself unto emptiness, and deigned to assume our likeness, should become for our sakes the pattern and way of every good work.
[...] In order therefore that we may learn both the power itself of holy baptism, and how much we gain by approaching so great a grace, He commences the work Himself.
Cyril of Alexandria (c. 376-444): Commentary on St Luke’s Gospel, Sermon 11.