Counting days is simple. The day/night cycle can be observed everywhere on Earth (except sometimes at the poles).
Counting months is more complicated. Though initially based on the lunar cycle of 29.5 days, one could not round off to 30 because 12 months of 30 days (360 days) do not add up to a year.
All of the difficulties arise from a year that does not contain a whole number of days. The Earth turns around the Sun in 365.2425 days, or practically 365 + ¼ days (365.25). If one ignores this ¼ day, one accumulates discrepancies which can end up placing the month of January in the middle of the summer (after 800 years).
It was in 46 BC, under the reign of Julis Caesar, that the leap year reform was undertaken. For this reason, this calendar was named the "Julian" calendar. It was again reformed in 1582 by Pope Gregory XIII.