They cannot say that the angel was Jehovah because “no man has seen God at any time.” However, they also cannot say that the angel was a manifestation of Jesus - because according to their belief He had no eternal pre-existence as Jesus. Therefore they maintain that these were Jehovah’s angelic representatives; but this is where the problems start because of the way they were treated.
The article [pp.21-23] first deals with Moses in Exodus 33:17-23 and rightly points out that God says, “You are not able to see my face, because no man may see me and yet live.” However, Moses was able to see the ‘back’ of God. The Society tells us that this is just the “afterglow of the divine presence.” We can probably accept that but an important point has been made - no man can see the face of God the Father and live - this needs to be applied to some of the other passages the article mentions.
For instance Exodus 3:2-6 where the Society says that this is just God’s angel but read the Scriptures carefully. In v.5, Moses is told to take off his shoes, as this is holy ground. And in v.6 he hears the words, “I am the God of your...” No angel would dare say that, he would have to say, the God who sent me...
Again, look at Judges 6:11ff where Jehovah’s angel appeared to Gideon but v.14 tells us Jehovah faced him. In v.15 Gideon addresses the angel as Jehovah and offers a sacrifice to Him. Both acts that an angel would refuse to accept
The Society concludes the article by saying that now we can
“Understand why Abraham addressed the materialized angelic spokesman of God as if he were talking to Jehovah God himself [Genesis 18:1.]"However, God is God and an angel is an angel and you cannot confuse them. Abraham, bowed down before them - v.2; this one is a life giver - v10; this one is able to read the heart - v.13; this one has the power to do what he wants - v17; Abraham intercedes to this one - v.23 etc; the ‘angel’ answered immediately what He would be willing to do - v.26. There is no way that we can intelligently read these verses without realising that Abraham was speaking to God - it was not possible for him to be speaking with an angel.
The Society claims that the angelic spokesman was like a radio or telephone transmitting God’s messages to men. But the radio or the telephone never claim to be the person who is speaking! We need to reconcile this matter satisfactorily from Scripture to show the falseness of the Society’s teaching. If no man has ever seen the face of God and yet this “Angel of the Lord” is God, don't we have an impossible situation? No, we do not but the Watchotwer Society does.
There is a very simple answer which means we do not have to stand Scripture on its head. No man has ever seen the face of God the Father but God has revealed Himself as God the Son. This “Angel of the Lord” was treated as God because He is God - here we have Jesus appearing on the earth before His birth at Bethlehem. The eternal Jesus, second part of the glorious Godhead manifesting Himself. No problems - just a willingness to read the Bible as it is written and not put our own man-made doctrines into it.