When recovering Copper from Copper Chloride via Aluminum, why can't we use Sodium instead to make Sodium Chloride?
As your teacher mentioned, sodium is a very reactive material. She mentioned that it is hard to obtain it naturally as a result. However, this isn't quite the reason as to why sodium isn't used for recovery. 

If we were to only consider the cost in energy, aluminum would be a poor choice.
The main process for production of aluminum metal requires a current of 400 kiloamperes and temperatures of 950 C. In contrast, the main process for sodium metal production requires a current of 30 kiloamperes and temperatures of 600 C. 

The main reason would be because sodium is too reactive to be used. The sodium metal would react with the water and form sodium hydroxide. This reaction would be too fast and violent that you wouldn't be able to recover copper.
So your teacher was right in pointing out that sodium is too reactive.