A - Thanks for the question. There are certainly problems with the quote. I am a big fan of CS Lewis, but we must remember that he had several things wrong, even when he had most things right.
Here is what the Catholic Church teaches about the body and soul, which is all based on the Incarnation - God taking on flesh.
A human person = body + soul
To be human means that we have both. Those creatures that are merely spiritual (without a body) are called angels. When we no longer have our bodies joined to our souls, this causes us to die. So, to say we merely "have a body" is a reflection of early Christian heresies, especially Manichaeism. Many of the early Church heresies were dualistic in nature. They taught the soul is the real person and bound for eternity, but the body is merely a shell that is to be used while on this earth.
But, this denies how humans are made and that the body has meaning. If the body has no meaning, then the Incarnation has no meaning. If the Incarnation has no meaning, then can Christ really save us from our sins?
This tendency to separate body and soul is still strong in modern Christianity, but we must fight for the goodness of the body, because in it is found our identity in Christ and His body, which was laid down on our behalf.
Vatican II taught:
“Though made of body and soul, man is one. Through his bodily composition he gathers to himself the elements of the material world; thus they reach their crown through him, and through him raise their voice in free praise of the Creator. For this reason man is not allowed to despise his bodily life, rather he is obliged to regard his body as good and honorable since God has created it and will raise it up on the last day. Nevertheless, wounded by sin, man experiences rebellious stirrings in his body. But the very dignity of man postulates that man glorify God in his body and forbid it to serve the evil inclinations of his heart." -GS 14John Paul II knew well the problems that had once again come into Christianity and the denigration of the body. He fought this anti-body mentality by writing his Theology of the Body. This is an anthem for the goodness of the body and a treatise on why the body is in need of redemption.
"We know that all creation is groaning in labor pains even until now; and not only that, but we ourselves, who have the firstfruits of the Spirit, we also groan within ourselves as we wait for adoption, the redemption of our bodies." - Romans 8:22-23