Astronomical year numbering
Cassini gave the following reasons for using a year 0:
Fred Espanak of NASA lists 50 phases of the moon within year 0, showing that it is a full year, not an instant in time. Jean Meeus gives the following explanation:
Although he used the usual French terms "avant J.-C." (before Jesus Christ) and "après J.-C." (after Jesus Christ) to label years elsewhere in his book, the Byzantine historian Venance Grumel used negative years (identified by a minus sign, −) to label BC years and unsigned positive years to label AD years in a table. He did so possibly to save space and put no year 0 between them.
Millennium
The "year 2000" has also been a popular phrase referring to an often utopian future, or a year when stories in such a future were set, adding to its cultural significance. There was also media and public interest in the Y2K bug. People liked to compared their odometer as a reason to celebrate the new millennium which goes from 1999 to 2000. Thus, the populist argument was that the new millennium should begin when the zeroes "rolled over" to 2000, i.e., the day after December 31, 1999. Some people thought that the change of the hundreds digit in the year number, and the zeros rolling over, created a sense that a new century had begun.