What are reasons why a pen is wiser then a pencil?

First, one should note that this is an essay prompt intended to have you think creatively. On a literal level, neither a pen nor a pencil is wise, as both are inanimate objects. 
On the most literal level, again, whether one prefers pen or pencil is a matter of individual choice and circumstance. The main difference between the two is that pen is much harder to erase, but more durable and easier to read.
If you want to argue that the pen should be the emblem of wisdom, there are several key points you could make:
Antiquity: While pens dipped in ink were used for writing on papyrus in ancient Egypt, the pencil was only invented in the sixteenth century due to the discovery of graphite.
Permanence: One would desire words of wisdom to be written in a durable form, and thus the pen is more appropriate due to ink lasting longer.
Readability: Dark ink from a pen is more opaque and thus more readable than writing in pencil and less prone to accidental smudging (once it has dried).
Writing speed: Because it is difficult to erase writing from pens, you must think carefully before you write, whereas with pencil (or, even more so, computers), your ability to correct easily may encourage you to write quickly without careful thought.