In Raphael and Picasso pay attention: God is not a man that he should lie (Numbers 23:19), I focused on the first half of Numbers 23:19, “God is not man, that he should lie, or a son of man, that he should change his mind.”
I argued that from “God is not a man,” or/and “God is not a son of man,” Jewish exegetes derive the following “watertight” conclusion:
Major premise: God is not a man.
Minor premise: Jesus is a man/a son of man
Conclusion: Therefore Jesus is not God.
What I’d like to show here is that although Judaism sees everything in this verse to prove that a man can never be God, Christians should rightly see nothing in this verse that could be used as evidence to either prove or disprove that God can never be a man. that is, take on flesh.
Here are verses 18 and 19 of Numbers 23:
 And Balaam took up his discourse and said,
“Rise, Balak, and hear;
give ear to me, O son of Zippor:
 God is not man, that he should lie,
or a son of man, that he should change his mind.
Has he said, and will he not do it?
Or has he spoken, and will he not fulfill it?
(Numbers 23:18-19 ESV).
According to rabbinical exegesis, the following imaginative scenario is consistent with their view. God speaks: “I’ve noticed that some/many/all of my people have this idea that I have arms and legs. Better put them straight. And while I’m about it, I’ll also tell them that I don’t lie, that I don’t change my mind, and that I do what I say; and no one with arms and legs, even with Hebrew arms and legs, better tell me otherwise.”
Numbers 23:19: “God is not a man that He should lie” יט לֹא אִישׁ אֵל וִיכַזֵּב
The verb “(vay)cha’zev” וִיכַזֵּב, refers to being unfaithful to one’s commitment.
Now, why would God want/need to inform his people that He doesn’t have arms and legs (“God is not a man…”)? I answer: the Israelites were not that dumb to think that the “arm of the Lord” meant that he has a physical arm. (Why Rambam, 15 centuries or so later, spent so much effort to hammer this Torah truism home beats me). It had also been drummed into the Israelites for centuries that God was NOT a man. Nor did Israel’s enemies believe that their gods were men, or supermen with very big muscles. For example, consider the Babylonians. When the King asked the magicians, the enchanters, the sorcerers to interpret his dream, they replied: “The thing that the king asks is difficult, and no one can show it to the king except the gods, whose dwelling is NOT OF FLESH” (Daniel 2:11).
In numbers 23, Balak is the King of Moab. The god of Moab was Molech. Although the Moabites had a statue with a big furnace for a stomach into which they threw children, they didn’t believe that Molech had a human body, or any other kind of body. Molech was the sun, or the fire that emanated from it.
Christians with any knowledge of basic grammar are not worried that Judaism uses Numbers 23:19 as a disproof text against their belief that God took on a human body. Judaism, on the other hand, milks the teats off the text to buttress its belief that God could never be a man.
To sum up, both the grammar and the historical context make it clear that God is not trying to prove that He does not have a body. Nothing as outré as that. God is merely saying – contra Judaeorum – that men (all men) and women (all women) lie and go back on their commitments, which is why human beings are not like God – why they need a Saviour. The New Testament reveals that the Saviour , the Son of God, took on flesh (John 1) which Christians celebrate this very day of Christmas:
[1:1] In the beginning was the Word, and the Word was with God, and the Word was God.  He was in the beginning with God.  All things were made through him, and without him was not any thing made that was made.  In him was life, and the life was the light of men.  The light shines in the darkness, and the darkness has not overcome it.  There was a man sent from God, whose name was John.  He came as a witness, to bear witness about the light, that all might believe through him.  He was not the light, but came to bear witness about the light.
 The true light, which enlightens everyone, was coming into the world.  He was in the world, and the world was made through him, yet the world did not know him.  He came to his own, and his own people did not receive him.  But to all who did receive him, who believed in his name, he gave the right to become children of God,  who were born, not of blood nor of the will of the flesh nor of the will of man, but of God.
 And the Word became flesh and dwelt among us, and we have seen his glory, glory as of the only Son from the Father, full of grace and truth (John 1:1-14 ESV).
God took on a body, an unblemished body, to save bodies and souls, sinful bodies and souls, from eternal fire.