Fur chewing can also be genetic as well.
Sometimes it can also be something new in their life stressing them out(diet, cagemate, placement of cage or cage size, etc...). I didn't know and I had my stereo playing for my chins (they get it 24/7). No crazy music, just classics...but an old timer who had raised chinchillas for 40 years came by my place one day. I asked for his help because I had one particular cage, that no matter what chinchilla I put in that cage, no matter their age, gender or whatever... they all chewed once they resided in that cage. Once they were put in another cage it stopped... Turned out that my friend pointed to the speakers and mentioned one was directed (even though it was nowhere near the cage but opposite end of a 30 ft room) toward that cage.
He explained the vibrations possibly or sound waves? from the speakers were causing it. When I directed the speakers to the wall....the chewing seized with any chin who lived in that cage afterwards. It happened many years ago, but it is a reminder to me, that the simplest things in life, can cause stress to chins who may in turn choose to chew, that we may never notice.