The "Angel of the LORD"--Jesus?

There are many times in the Old Testament where God is described as an angel. See Exodus 23:20-21 from today's reading as well as my post on this topic from last year. In the post last year I mentioned how I'd heard somewhere that the angel of the LORD was not only God, but more specifically the second person of the Trinity--he who would come to earth as Jesus Christ to save us from our sins. But why do they identify this angel as the second person of the Trinity?

I think I might have finally found that answer today, ten months later. The Kretzmann commentary on Exodus 23:20-21 says, "This special guiding and protecting Angel was the Son of God Himself, for in Him Jehovah was revealed; in Him, as the Angel of the face of God, the innermost essence of God was manifested." In other words, the second person of the Trinity is defined as God revealing himself personally to us, just as Jesus would do in the New Testament.