How do Trinitarians respond to the objection that God cannot be a man based on Hosea 11:9?

The irony is that in verse 1 of chapter 11,

When Israel was a child, I loved him, and out of Egypt I called my son.

we can see that Christ's first coming would be in union with Israel as the Son of God fleeing to Egypt and being called out of Egypt (11:1; cf. Matt. 2:13-15).

This indicates that although Israel became exceedingly evil, Christ still became organically one with them through incarnation to be a real Israelite. Christ is the Son of God, and the Israelites were sons of God. Christ joined Himself to them in this matter of being sons of God.

God, including Jesus, was in no way human at the time the Old Testament was written. It was only after the incarnation that Jesus took on flesh. However, in Old Testament times there were theophanies/Christophanies, where God/Christ appeared as a burning bush, an angel, or a man. But though those things were visible, Christ did not take on human nature at that time, any more than He took on vegetable nature as a burning bush.

God was manifested in flesh [TR - KJV : 1 Timothy 3:16]

Jesus Christ is come in the flesh [1 John 4:2 KJV]

That God is manifested in flesh and that Jesus Christ is come in the flesh is not at all the same as to say that 'God is a man'.

The scripture, in the original Greek, is exceeding careful in this aspect and although I support the KJV yet still I have to find fault with it, where, on occasion, it adds the word 'man' in connection with Jesus Christ where neither the word anthropos (humanity) nor aner (an identifiable individual man) nor arrhen (a solitary man, a bachelor) appear in the original, the correct translation sometimes, for example, being 'one', not 'man', as in Hebrews 3:3..

Thus also, the expression 'God was made man' or 'God became man' (which I have heard and read) are not scriptural. God was not changed into humanity.

So the text in Hosea 11:9 holds good in the New Testament, for 'manifest in flesh' or 'come in flesh' do not at all have the same meaning as 'I am a man'. Thus God says 'I am not a man', quite rightly and quite consistently.

But the manifestation was promised from the beginning. In Eden, God promised that the seed of the woman would bruise the head of the serpent, that is to say, from above, in ascension, and that in humanity, Genesis 3:15.

Thus the Arche, the Principality, the anointed cherub on the holy mountain, Ezekiel 28:14, is bruised by the Lord, manifest in humanity.

And manifestation is seen again in the three men who came to Abraham and he said, My Lord, and bowed himself to the ground, Genesis 18:2.

And again, when Jacob wrestled with a man to the breaking of the day and he would not tell him his name, but touched his thigh and the sinew shrank, Genesis 32:24.

And again when Manoah and his wife saw the Angel of the Lord caught up in the flame, Judges 13;20.

An yet again, when Moses beheld the Angel of the Lord call out to him from the manifestation of a bush that burned and was not consumed, Exodus 3:2, a picture of deity manifest in humanity, the humanity not consumed by him who is a consuming fire.

And yet again when the king saw a fourth in the furnace and he was like unto the son of God, Daniel 3:25.

These manifestations heralded the coming of the Son of man, that is to say - The Son; of man - who would 'come of woman', Galatians 4:4.

It was ever intended.

And it is so.

But without contradiction, for God is not a man. But God is, in the person of the Son, manifest in flesh and come in flesh and come of woman.

There are two or three passages in the Old Testament which declare something similar (Numbers 23:19 and 1 Samuel 15:29). In each case God is distinguishing himself against sinful humanity. The point is that it is his actions which are different from a man's.

At the same time, Jesus himself said "God is Spirit" (John 4:24). The Bible consistently affirms there is a difference between the Creator and the created (the Creator-creature distinction). Jesus is on the 'Creator' side of that divide (John 1:3). The wonder of the incarnation is not that God is just the same as us, but rather the perfect and holy Son of God became one of us.

As the Athanasian Creed puts it:

For the right Faith is that we believe and confess: that our Lord Jesus Christ, the Son of God, is God and Man;
God, of the Substance of the Father, begotten before the worlds: and Man, of the Substance of his Mother, born in the world;
Perfect God, and Perfect Man: of a reasonable soul and human flesh subsisting;
Equal to the Father, as touching his Godhead: and inferior to the Father, as touching his Manhood.
Who although he be God and Man: yet he is not two, but one Christ;
One, not by conversion of the Godhead into flesh: but by taking of the Manhood into God;
One altogether, not by confusion of Substance: but by unity of Person.
For as the reasonable soul and flesh is one man: so God and Man is one Christ.