Introduction

There are some faith traditions which erroneously claim Jesus had only a human nature. Yet, it is without question that Jesus claimed to be the Messiah (Jn. 4:26). He fulfilled the Messianic prophecies (Mt. 11:3-5; Lk. 7:22-23; Lk. 4:18-21). He is denoted by Messianic names, "king of Israel" (Lk. 19:38), "Son of David" (Mt. 9:27), "Son of man", "he that cometh in the name of the Lord" (Mt. 21:9). Moreover, Jesus claims to be greater than Abraham (Jn. 8:53,56), than Moses (Mt. 19:8-9), than Solomon and Jonah (Mt. 12:41-42); He claims to be sent by God (Jn. 5:36-37,43), calls God His Father (Lk. 2:49), and He accepts the titles "Master" and "Lord" (Jn. 13:13-14). He forgives sin in answer to the observation that God alone can forgive sin (Mk. 2:7,10; Lk. 5:21,24). He acts as the Lord of the Sabbath (Mt. 12:8), and tells Peter that as "Son" He is free from the duty of paying temple tribute (Mt. 17:24,25). He allows Nathanael to call Him "Son of God" (Jn. 1:49). The apostles (Mt. 14:33) and Martha (Jn. 11:27) give Him the same title. Twice He approves of Peter calling Him "the Christ, the Son of God" (Jn. 6:69), "Christ, the Son of the living God" (Mt. 16:16). Four distinct times does He proclaim Himself the Son of God; to the man born blind (Jn. 10:30,36); and to the two assemblies of the Jewish Sanhedrin (Mt. 26:63-64; Mk. 14:61-62; Lk. 22:70). Jesus applies to Himself, and allows others to apply to Him, the title "Son of God" in its full meaning. An eagle begets an eagle. A lion begets a lion. That which is begotten, takes on the nature of the parent. So too, the eternally begotten son of God the Father, is God the Son. If there had been a misunderstanding Jesus would have corrected it, just as Paul and Barnabas corrected those who mistook them for gods (Acts. 14:12-14).

Catechism
The Church thus confesses that Jesus is inseparably true God and true man. He is truly the Son of God who, without ceasing to be God and Lord, became a man and our brother: "What he was, he remained and what he was not, he assumed", sings the Roman Liturgy and the liturgy of St. John Chrysostom proclaims and sings: "O only-begotten Son and Word of God, immortal being, you who deigned for our salvation to become incarnate of the holy Mother of God and ever-virgin Mary, you who without change became man and were crucified, O Christ our God, you who by your death have crushed death, you who are one of the Holy Trinity, glorified with the Father and the Holy Spirit, save us!"
- Catechism of the Catholic Church, 2nd ed., (1997), n.469
The Incarnation is therefore the mystery of the wonderful union of the divine and human natures in the one person of the Word.
- Catechism of the Catholic Church, 2nd ed., (1997), n.483
Scripture

Ex. 3:14 - In the Old Testament, God reveals His name as "I AM who AM".

Jn. 8:24,58 - In the New Testament, Jesus says of Himself, "Before Abraham was, I AM".

Lk. 1:31-32 - The angel of the Lord proclaims Jesus as Son of the Most High.

Mt. 2:2,11; Mt. 8:2; Mt. 14:33; Mt. 28:9; Mt. 28:17; Lk. 24:52; Jn. 9:38 – Jesus allows Jews to worship Him. Only God can be worshipped.

Mt. 9:2; Mk. 2:5; Lk. 5:20; Lk. 7:48 – Jesus forgives sins. Only God can forgive sins.

Mt. 4:7; Lk. 4:12 – Jesus tells Satan, "you shall not tempt the Lord your God" in reference to Himself.

Mt. 12:8; Mk. 2:28; Lk. 6:5 - Jesus says that He is "Lord of the Sabbath." He is the Lawgiver. He is God.

Mt. 26:63-64; Mk. 14:61-62; Lk. 22:70; Jn. 10:30 - Jesus claims to be the Son of God.

Jn. 1:1; Rev. 1:8; Rev. 22:12-13 - John says the Word and God are one. Jesus Christ is the Word; the Alpha and Omega.

Jn. 20:28 - St. Thomas addresses Jesus as "My Lord and my God!".

Tradition & Fathers
"Having first said all these things, baptize into the name of the Father, and of the Son, and of the Holy Spirit..."
- Didache Apostolorum (A.D. ~90)
"… having learned that He[Jesus] is the Son of the true God Himself, and holding Him in the second place, and the prophetic Spirit in the third, we will prove."
- St. Justin Martyr, First Apology (A.D. ~110-165)
"Wherefore also I praise Thee for all things, I bless Thee, I glorify Thee, along with the everlasting and heavenly Jesus Christ, Thy beloved Son, with whom, to Thee, and the Holy Ghost, be glory both now and to all coming ages. Amen."
- Martyrdom of Polycarp (A.D. 157)
"For with Him were always present the Word and Wisdom, the Son and the Spirit, by whom and in whom, freely and spontaneously, He made all things, to whom also He speaks, saying, 'Let Us make man after Our image and likeness;' He taking from Himself the substance of the creatures [formed], and the pattern of things made, and the type of all the adornments in the world."