Christ's death also dealt with the old man. In ourselves we all are old because we belong to the old man. The old man is not the originally created man, but the fallen created man.
Romans 6:6a says that our old man has been crucified with Christ. This includes everything related to our old man, such as our thinking, our likes and dislikes, and our good temper and bad temper.
Christ's death terminated the old creation, which is related to the world. Galatians 6:14 says that the world was crucified on the cross. Then verse 15 says, "For neither is circumcision anything nor uncircumcision, but a new creation is what matters." This shows that the crucifying of the world is related to the new creation. If we do not go through the cross, we cannot be a new creation. On one side of the cross is the old creation, and on the other side is the new creation. When we pass through the cross, the old creation becomes the new creation.
In our life-study of the book of Daniel, I pointed out that the crucifixion of Christ, the Messiah, the Anointed One (Dan. 9:26), is a landmark between the old creation and the new creation. The old creation was terminated on the cross at Christ's death, so Christ's death becomes a landmark between the old creation and the new creation. We were the old creation, yet we have all been brought to the cross. On the cross we were terminated, and this termination ushered us into Christ's resurrection in which we all have been germinated to become the new creation. The new creation needs the crossing out of the old creation.