Carrots develop a rubbery skin due to moisture loss during storage, causing them to become dehydrated and flexible. This is the carrot's way of trying to protect itself.
When carrots are stored, they naturally lose moisture through transpiration. If the surrounding environment is dry, this moisture loss accelerates. As the carrot dehydrates, the outer layers become less rigid and more pliable, resulting in a rubbery texture. The carrot is essentially trying to conserve what little moisture it has left by forming a protective, albeit rubbery, barrier. This process is similar to how our skin wrinkles when we're dehydrated. The carrot's cells lose turgor pressure (the pressure of water inside the cells pushing against the cell wall), leading to the change in texture. Proper storage conditions are crucial to prevent this from happening.
To prevent carrots from becoming rubbery, store them in a sealed plastic bag in the refrigerator's crisper drawer. Adding a damp paper towel to the bag can further help maintain humidity and prevent moisture loss.