The Link Between Sin and Death
The link between sin and death is a more powerful one than at first appears. When the first man sinned, he brought death into the world, and this became a part of the world experience. We die because of sin, but the mechanism for this is that we are born into a world where sin and death reign. This is why Jesus could die - he was born into a world which was full of sin. Even though he did not commit any sin himself he still suffered from the curse of death which was passed on mankind as a result of sin.
This link is explained more fully in the section God's Plan, which describes God’s plan and purpose for the world.