It is really an interpretation of some in Christendom that God himself became flesh. No bible writer teaches this. Some believe this because of a scribal change to 1Ti 3:16, but Catholic bibles don’t have this defect, like the KJV that has God where the word he is found below.
NJB 1 Timothy 3:16 Without any doubt, the mystery of our religion is very deep indeed: **He **was made visible in the flesh, justified in the Spirit, seen by angels, proclaimed to the gentiles, believed in throughout the world, taken up in glory.
Another place where some appeal is **John 1:14 **where it was the Word who was made flesh and not God himself. Because of their interpretation that the Word is identified as God as opposed to having divinity predicated upon him they view this as God himself becoming flesh. That is an interpretation and not something bible writers explicit teach.
The only place I can think of where Paul might be said to be responsible for this teaching is Col 2:9. However bibles like the NAB correctly show that the word SWMATIKOS is an adverb and not a noun as in some renderings where they use the term “bodily form”.
NAB Colossians 2:9 For in him dwells the whole fullness of the deity bodily,
This could mean plenty of things, none of which are that God himself dwells in a human body.