Explain why a lunar calendar would be inaccurate?

A lunar calendar is dependent upon the phases of the moon and the phases of the moon is the same phases per each lunar month, as it has been for thousands of years.

Ancient civilizations throughout history have only used a lunar calendar for thousands of years, which is 10x older than the roman christian "Gregorian" solar calendar that were presently using today. So no, the lunar calendar is not inaccurate. The purpose of the creation of the moon, was to tell time, as it was created to be a watch in the sky.

Ecclesiasticus 43:6 (Apocrypha)

He made the moon also to serve in her season for a declaration of times, and a sign of the world.