I thought I may deal with the subject of Genesis 18 but also deal with the subject of Isaiah 7:10-14 together and to see if the subject of Jesus being the angel of the LORD is refuted.
Let's recap the points about Genesis 18 and add additional points to it.
Here is Genesis 18 in context:
"The Three Visitors
18 The Lord appeared to Abraham near the great trees of Mamre while he was sitting at the entrance to his tent in the heat of the day. 2 Abraham looked up and saw three men standing nearby. When he saw them, he hurried from the entrance of his tent to meet them and bowed low to the ground.
3 He said, “If I have found favor in your eyes, my lord,[a] do not pass your servant by. 4 Let a little water be brought, and then you may all wash your feet and rest under this tree. 5 Let me get you something to eat, so you can be refreshed and then go on your way—now that you have come to your servant.”
“Very well,” they answered, “do as you say.”
6 So Abraham hurried into the tent to Sarah. “Quick,” he said, “get three seahs[b] of the finest flour and knead it and bake some bread.”
7 Then he ran to the herd and selected a choice, tender calf and gave it to a servant, who hurried to prepare it. 8 He then brought some curds and milk and the calf that had been prepared, and set these before them. While they ate, he stood near them under a tree.
9 “Where is your wife Sarah?” they asked him.
“There, in the tent,” he said.
10 Then one of them said, “I will surely return to you about this time next year, and Sarah your wife will have a son.”
Now Sarah was listening at the entrance to the tent, which was behind him. 11 Abraham and Sarah were already very old, and Sarah was past the age of childbearing. 12 So Sarah laughed to herself as she thought, “After I am worn out and my lord is old, will I now have this pleasure?”
13 Then the Lord said to Abraham, “Why did Sarah laugh and say, ‘Will I really have a child, now that I am old?’ 14 Is anything too hard for the Lord? I will return to you at the appointed time next year, and Sarah will have a son.”
15 Sarah was afraid, so she lied and said, “I did not laugh.”
But he said, “Yes, you did laugh.”
Abraham Pleads for Sodom
16 When the men got up to leave, they looked down toward Sodom, and Abraham walked along with them to see them on their way. 17 Then the Lord said, “Shall I hide from Abraham what I am about to do? 18 Abraham will surely become a great and powerful nation, and all nations on earth will be blessed through him.[c] 19 For I have chosen him, so that he will direct his children and his household after him to keep the way of the Lord by doing what is right and just, so that the Lord will bring about for Abraham what he has promised him.”
20 Then the Lord said, “The outcry against Sodom and Gomorrah is so great and their sin so grievous 21 that I will go down and see if what they have done is as bad as the outcry that has reached me. If not, I will know.”
22 The men turned away and went toward Sodom, but Abraham remained standing before the Lord.[d] 23 Then Abraham approached him and said: “Will you sweep away the righteous with the wicked? 24 What if there are fifty righteous people in the city? Will you really sweep it away and not spare[e] the place for the sake of the fifty righteous people in it? 25 Far be it from you to do such a thing—to kill the righteous with the wicked, treating the righteous and the wicked alike. Far be it from you! Will not the Judge of all the earth do right?”
26 The Lord said, “If I find fifty righteous people in the city of Sodom, I will spare the whole place for their sake.”
27 Then Abraham spoke up again: “Now that I have been so bold as to speak to the Lord, though I am nothing but dust and ashes, 28 what if the number of the righteous is five less than fifty? Will you destroy the whole city for lack of five people?”
“If I find forty-five there,” he said, “I will not destroy it.”
29 Once again he spoke to him, “What if only forty are found there?”
He said, “For the sake of forty, I will not do it.”
30 Then he said, “May the Lord not be angry, but let me speak. What if only thirty can be found there?”
He answered, “I will not do it if I find thirty there.”
31 Abraham said, “Now that I have been so bold as to speak to the Lord, what if only twenty can be found there?”
He said, “For the sake of twenty, I will not destroy it.”
32 Then he said, “May the Lord not be angry, but let me speak just once more. What if only ten can be found there?”
He answered, “For the sake of ten, I will not destroy it.”
33 When the Lord had finished speaking with Abraham, he left, and Abraham returned home."
Now, here are my points from Contra Blumenthal on this issue about the angel of the LORD:
"While you are free in the matter to suggest that the angel is a representative, this wouldn't undercut Jesus being God and appearing to the people as an angel FUNCTIONALLY. Jesus is Ha Shem, but he is not the Father, however this wouldn't detract from the fact he can function as the Father's agent or his representative. It's one member of the Trinity speaking on behalf of another, like in the examples that were given by Blumenthal himself where a representative can speak on God's behalf. If Jesus himself is YHWH, then he is worthy of the devotion that is given to God, considering he is in nature God (Philippians 2:5-11) but is a distinct person from the Father. If however he is not God, I think Jews and Christians already know the answer to that one."
To add to this, Jesus is a man, but that wouldn't refute him being God. Jesus existed eternally with the Father. His human body is created, not his divine nature. Jesus being God wouldn't refute him being a man and vice versa. John 1:1 and Philippians 2:5-11 being prime examples of the deity of Jesus. If you read Philippians 2, it says:
"6 Who, being in very nature[a] God,
did not consider equality with God something to be used to his own advantage;
7 rather, he made himself nothing
by taking the very NATURE OF A SERVANT,
being made in human likeness.
8 And being found in appearance as a man,
he humbled himself
by becoming obedient to death—
even death on a cross!
9 Therefore God exalted him to the highest place
and gave him the name that is above every name,
10 that at the name of Jesus every knee should bow,
in heaven and on earth and under the earth,
11 and every tongue acknowledge that Jesus Christ is Lord,
to the glory of God the Father.". He takes the form of a slave and set aside his divine perogatives while he was on earth."
He didn't exist as a man before man existed. He didn't take on flesh until 2000 or so years ago. Jesus appeared to Jacob in the form of a man, it was temporary and wasn't a true incarnation. It's not until the time of the NT that he had a physical body.
There is a difference between taking on flesh and taking on appearance of a man. The angels appeared as men in Genesis 18, but we know they aren't men. Likewise, Jesus appeared to Jacob, but only appeared as a man, rather than have a true incarnation centuries later.
One of the angels in Genesis 18-19 doesn't head down to Sodom and Gomorrah, the other two go down there, hence one of the men or angels who appeared to Abraham is God, who stayed with Abraham and spoke with him. The two men were angels ontologically, whereas Christ functioned as an angel.
Two of the men go down to Sodom and Gomorrah but one doesn't and stays near Abraham, then leaves after the conversation. Obviously, angels and prophets are not synonymous with God, however my claim is that there is a particular angel in the TANAKH who functions as an angel, but is in nature God.
Let's take a look at Isaiah 7:10-14:
"6 “Let us invade Judah; let us tear it apart and divide it among ourselves, and make the son of Tabeel king over it.” 7 Yet this is what the Sovereign Lord says:
“‘It will not take place,
it will not happen,
8 for the head of Aram is Damascus,
and the head of Damascus is only Rezin.
Within sixty-five years
Ephraim will be too shattered to be a people.
9 The head of Ephraim is Samaria,
and the head of Samaria is only Remaliah’s son.
If you do not stand firm in your faith,
you will not stand at all.’”
10 Again the Lord spoke to Ahaz, 11 “Ask the Lord your God for a sign, whether in the deepest depths or in the highest heights.”
12 But Ahaz said, “I will not ask; I will not put the Lord to the test.”
13 Then Isaiah said, “Hear now, you house of David! Is it not enough to try the patience of humans? Will you try the patience of my God also? 14 Therefore the Lord himself will give you[c] a sign: The virgin[d] will conceive and give birth to a son, and[e] will call him Immanuel.[f]"
Isaiah does function as an agent but this is a different context to Genesis 18, since Isaiah himself isn't being identified as God, but in the context of Genesis 18, The angel is identified as God explicitly and Abraham even stood before him and talked with him as a regular person. Isaiah was merely used as a mouthpiece to convey the words of God to Ahaz and tell him what will transpired. These are two different contexts and do not refute Jesus being the angel of YHWH, nor do they prove that Isaiah is synonymous with God himself. There isn't inconsistency or lack of consistency here.
Hope I have answered the objection.