In many places, you teach that the Angel of the Lord is always the Second Person of the Godhead, that is the pre-incarnate Christ. How do you know this is to be so?
Scripture clearly shows the Angel of the Lord is the part of the Godhead, and in particular the pre-incarnate Christ.
The term “the Angel of the Lord” first appears in Genesis 16:
Notice a few things here. First, the Angel of the Lord tells Hagar that He will “greatly multiply your descendants.” An ordinary angel cannot do that, for only the Lord God can give life (Deuteronomy 32:39). Also, this statement is very similar to what God told Abraham (Genesis 15:5).
Second, the Angel of the Lord knew Hagar was with child, that the child was a son, and what he would be like. Only God is omniscient to know the future (e.g., Hebrews 4:3), though ordinary angels can be told the future by God.
Third, in v. 11, the angel says “the LORD has given heed to your affliction” when it was the Angel of the Lord who had given heed.
Finally, in v. 13, the text says “the name of the LORD who spoke to her," clearly indicating that Hagar was speaking to God. Furthermore, Hagar calls the Angel "God" and can’t believe she remained alive after seeing Him! Indeed, the word Beer-lahai-roi means, “well of the Living One seeing me.”
Next, we look at Genesis 22:
In both of these passages, it’s clear that the Angel of the Lord is also God. In v. 12 He says you have not withheld your son “from Me,” obviously referring to God. In vs. 15 and 16, the Angel of the Lord says of Himself “by Myself…declares the Lord.” Again, it’s clear the Angel of the Lord and God are One and the same.
Next, consider Exodus 3:
The Angel of the Lord in v.2 is clearly equated with God in v.4. In v.6, He makes clear He is the God of Abraham, Isaac, and Jacob, and Moses understands, for he is afraid to look at God (remember Hagar above).
There are many, many more passages that demonstrate that the Angel of the Lord is, in fact, God Himself.
But how do we know this appearance of God is always the pre-incarnate Jesus?
First, we know the Godhead is the Father, the Son, and the Holy Spirit, but in John 6: 46, Jesus says, “46 Not that anyone has seen the Father, except the One who is from God; He has seen the Father.” Since no one has seen the Father, and since people did see the Angel of the Lord, we can, therefore, know that the angel of the Lord cannot be the Father.
Second, the Holy Spirit never takes human form, and rarely does the Spirit take any form. He took the form of a dove when Jesus was baptized (Matthew 3:16), and as tongues of fire at Pentecost (Acts 2:3-4), but He is never shown in scripture to assume the form of man. Therefore, we have no reason to assume these OT appearances of the Angel of the Lord are the Spirit.
Finally, Paul says that Jesus has always been the "image of the invisible God" in Colossians:
Consequently, the Angel of the Lord is the image of the invisible God in the days before Jesus took on flesh, which is why we say He is the “pre-incarnate” Christ. Furthermore, the Angel of the Lord never appears in the New Testament, once Jesus took on flesh (became incarnate), nor after His resurrection. The only mention of such a person in the New Testament is described as “an” angel of the Lord, but never “the” Angel of the Lord. Once God the Son appeared as flesh, there was no longer a need for Him to appear in any other form as “the Angel of the Lord”.
Finally, it's interesting to consider that the word “angel” means messenger. A messenger is one who is sent from someone else to deliver a message, and of course, Jesus fits this perfectly. He says in John 8:18, “I am He who testifies about Myself, and the Father who sent Me testifies about Me.” Just as the Father sent Jesus, so also did He send the Angel of the Lord. Based on all the above, we conclude that the pre-incarnate Lord Jesus was the Angel of the Lord.