The following is a rough idea and my explanation may be not detailed or not exact enough:

As I state in my New Testament commentary, Christ is the radio waves (well, not only radio but also other parts of the spectrum) of the universe. Christ is also the truth (the true information contained in the cosmic radio waves).

When information passes through the sin, it is damaged, that is loses its content.

Christ is the only kind of information which can pass through the sin without being damaged.

So in likeness of sinful flesh it appeared the essential content of cosmic radio waves. All other kinds of information except of Christ has faded away, but Christ has appeared in likeness of sinful flesh, without any damage but remaining true.

This way, despite of being bad, sin reveals Christ, filtering away anything other.

Get my rough idea on how Christ is related with sin.