I was writing down a chemical equation with my pencil and noticed its pungent smell. Could graphite itself be the reason for it?
None of the carbon allotropes have a smell. If you smell something from a pencil lead (graphite), then it will be from the impurities in it.
Graphite is made from impure organic compounds that frequently contain sulphur. It is likely that you are smelling this. Mercaptans and other sulphur compounds can be very smelly. on its own