I think we need to be careful of circular logic here. The ocean is water, ice cubes are water, therefore all oceans are ice cubes.
Some humans give messages, some angels give messages, therefore all messengers are angels.
Humans are not angels and angels are not humans. Nor does one ever become the other.
I am not completely against logic for I know that all of us including me use at times, but in the things of God it is NOT the Way to God's Truth:
"Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me." John 14:6
Jesus made it clear what "truth" was, but for you or me or anyone to accept and believe his statement is not done by logic, but by faith. Someone who does not know the Lord might be able to make a pretty good case against receiving his words based on logic alone, because they may seem to be self-serving.
As to the OT word,
angel, (for example as used in Gen 16:7) [4397, Hebrew = mal' ak], itself is translated in the KJV to the English word
angel 111 times. The same Hebrew word is translated to the English word,
messenger, 98 times, and 4 times it is translated as
ambassadors.
In the NT the word,
angel, (for example as used in Matt 1:20) [32, Greek = aggelos], itself is translated in the KJV to the English word,
angel 179 times. The same Greek word is translated to the English word,
messenger, 7 times.
Probably we can agree that it can mean
messenger but whether it excludes human messengers would not be so clear, would it, at least not without going through the particular uses in scripture? I am not linguist and have little personal knowledge of the original languages. I used on a Bible computer program to obtain the details listed in this post.
The first example I see in the OT is Gen 32:3, "And Jacob sent
messengers before him to Esau his brother unto the land of Seir, the country of Edom."
The Hebrew word translated as messenger in Gen 32:3 verse is the same one translated as
angel in Gen 16:7, "And the
angel of the LORD found her by a fountain of water in the wilderness, by the fountain in the way to Shur."
In the Greek of the NT notice for example the two following verses:
"But while he thought on these things, behold, the angel of the Lord appeared unto him in a dream, saying, Joseph, thou son of David, fear not to take unto thee Mary thy wife: for that which is conceived in her is of the Holy Ghost." Matt 1:20
"For this is he, of whom it is written, Behold, I send my messenger before thy face, which shall prepare thy way before thee." Matt 11:10
The Greek word translated as angel in Matt 1:20 is the same Greek word translated as messenger in Matt 11:10. [32, Greek = aggelos]
Matt 11:10 is speaking of John the Baptist, who we hopefully agree was a human being of flesh and blood similar in that respect to you and I. The reference to John the Baptist is quotation or paraphrase of Malachi 3:1 which reads:
"Behold, I will send my
messenger, and he shall prepare the way before me: and the Lord, whom ye seek, shall suddenly come to his temple, even the messenger of the covenant, whom ye delight in: behold, he shall come, saith the LORD of hosts."
The Hebrew word translated as
messenger in Mal 3:1 is the same word translated as
messengers in Gen 32:3 and as
angel in Gen 16:7.
What does all this prove? To me it simply raised some questions. The proof is to be found in accord with where the Holy Spirit leads.