So, she was afraid of herself, and what she could become. It's something that he could work with. A more selfless fear in that she didn't want to hurt others. Rey has all the potential to be a Jedi. If only she is well trained.

"Once you learn how to let go, you will also learn restraint. It will take patience and discipline, but it can be done. Only if you are willing."

This is why the Jedi began their training as young children. To prevent attachments, fears, and anything else that would hinder them. However, in this case there was no such luxury.