1 They are stressed
Being stressed or going through a stressful phase can be manifested through nail-biting or chewing on the end of pens, which is relieving for some people. (See Why do type A personalities get stressed?)
2 It helps them concentrate
Some people find chewing on pens to help them concentrate when they're studying or sitting for an exam.
3 They are nervous
When a person is nervous during an exam, they might chew on their pens to relieve this tension. (See The Body Language of Anxiety)
4 It relieves pain
Some people chew on their pens to relieve headaches or jaw pain from temporomandibular joint disorder (TMD).
5 They're bored
Some people resort to bad habits when they're bored such as biting their fingernails or chewing on their pens.
6 They're trying to quit a bad habit
Some people start chewing on pens when they're trying to quit a bad habit such as smoking. In this case, chewing on a pen is a distraction from craving cigarettes.
7 They zone out
Some people chew on their pen when they zone out and stop focusing on a certain thing. In this case, the chewing is done unconsciously.