Why will the difference between the Julian and Gregorian calendars become 14 days in 2100?

The premise that the difference between the Julian calendar and the Gregorian calendar will become 14 days in 2100 is correct.1

This shift occurs because of the different rules each system uses to calculate leap years. The Julian calendar adds a leap day every four years without exception, resulting in an average year length of 365.25 days. Because the actual solar year is approximately 365.2422 days, the Julian calendar gains time relative to the seasons at a rate of about one day every 128 years.21

The Gregorian calendar corrects this by omitting leap days in century years that are not divisible by 400. Under this rule, the year 2000 was a leap year, but 2100 will not be. While the Julian calendar will count February 29, 2100, as a leap day, the Gregorian calendar will treat it as a common day. This divergence increases the cumulative discrepancy between the two calendars from the current 13 days to 14 days.231