The Apostle John places an emphasis on flesh as polemic against the Gnostic idea that everything pertaining to the physical or material world is inherently corrupt. Docetists maintained that the the body of Jesus Christ was not real but illusionary. The suffering that He underwent on the cross was only apparent. In contrast, John expresses the true humanity of Christ. Consider also these statements from other writings by the same apostle:
"By this you know the Spirit of God: Every spirit that confesses that Jesus Christ has come in the flesh is of God, and every spirit that does not confess that Jesus Christ has come in the flesh is not of God. And this is the spirit of the Antichrist, which you have heard was coming, and is now already in the world." (1 John 4:2-3, emphasis added)
"For many deceivers have gone out into the world who do not confess Jesus Christ as coming in the flesh. This is a deceiver and an antichrist." (2 John 7, emphasis added)
During the Old Testament, God dwelt in the tabernacle and the temple (Exodus 25:8-9; 40:34-38; 1 Kings 8:10-11, 27). In the New Testament, this concept finds its place in Christ taking on human flesh.
Just as God the Father is not a father to Christ in the same sense of a parent to child relationship, the Son is not a son of God in the same sense as we are sons of God. There exists a unique relationship between God the Father and God the Son. Our special status as sons of God is given to us by adoption, and we cannot become divine.
The phrase "full of grace and truth" should be understood in light of its Old Testament backdrop of God's relationship with Israel (Exodus 34:6-7). Christ has the same characteristics. He is loving, merciful, and just.
Christ took on human flesh so that He can experience suffering and death. His divinity enabled Him to pay an infinite debt of sin. That is something which we could never do.