Our spirit is born of God thus making us children of God. The new creation we are in Christ is our spirit, obviously we still have our old bodies. "The new creation has been created in God’s image. It is righteous and holy" (Ephesians 4:24). Our spirit is born of God and is sinless and perfect.
"No one who is born of God sins." (1 John 5:18)
"By one offering He has perfected for all time those who are saints" (Hebrews 10:14).
"Because Christ died for all we no longer regard anyone according to the flesh" (2 Corinthians 5:16). We are to identify ourselves by our spirit. Thus we "put off the old man," no longer identify with him thus serving the flesh and "put on the new man," regard ourselves as we really are in the spirit as righteous, holy, sinless, perfect, & much more.
Romans 6:6 says, "Our old man is crucified with Jesus." The old man is already dead and gone so "putting off the old man" is putting him off of our mind. "Putting on the new man" is putting him on our mind and all the goodness that God has created in him.
To walk in the spirit is to walk according to the truth about your new spirit. You allow God to renew your mind so it will trust in the truth of who your Father has made you. A Child of God doesn't strive to win but rests in the victory of their loving Father and their older brother Jesus.