Why is this miracle so important to some?
And this is one reason for Jesus' miracles: For those who do not trust that God will take care of us. In other words, we need to be impressed. They need to see something extraordinary before we can trust that the Supreme Being is in control, and He can send His representative.
Jesus was showing them that they can rely on God.
"You of little faith, why did you doubt?" (Matt. 14:31)
The physical world is the perfect school.
It is a training ground, complete with consequences. When we do something that helps others, we are rewarded with the consequences of helping others. When we do something that hurts others, we are punished by the consequences of that action. In both instances, we are being taught by the physical environment so that we can grow.
Adam died spiritually
What is a "garment of skin?"
Most depictions of this event show Adam suddenly getting an animal skin to wear. But the text does not say he was given an animal skin. He says they were given "garments of skin."
Furthermore, "to work the ground from which he had been taken" illustrates that the body Adam was given came from the physical world ("ground").
The bottom line of this affair is that if Adam had trusted that God was telling him not to eat the analogous fruit of envy for his own good he would not have eaten it. Rather, Adam did not trust that God had his interest at heart. Adam doubted God, and distrusted God.
This same distrust exists within us even as we are in these physical bodies. We distrust when God comes to ask us to come home to Him. We distrust God's representatives when they tell us that God will take care of us and we can rely upon Him.
Distrust keeps us away from God
“‘Love the Lord your God with all your heart and with all your soul and with all your mind.' This is the first and greatest commandment.” (Matt. 22:37-38)