A calendar is a shared fiction, and occasionally somebody edits it. When that happens, real dates simply stop having happened.
Rome, 1582. Pope Gregory XIII issued Inter gravissimas to correct a drift of ten days that had accumulated since the Julian calendar was set up. In the countries that adopted it immediately, Thursday 4 October was followed by Friday 15 October. Ten dates were removed. But look closely at that sentence: Thursday was still followed by Friday. The weekday cycle was deliberately left intact. Nobody lost a Sunday.
Britain, 1752. Britain and its colonies held out for 170 years, by which point the error had grown to eleven days. Wednesday 2 September was followed by Thursday 14 September. Again, the weekday cycle survived. This is also why George Washington has two birthdays on record.
Stockholm, 1712. Sweden did the opposite of everybody else. Rather than deleting days it decided to phase the change in gradually, skipping every leap day for forty years — then got distracted by a war and forgot to skip 1704 and 1708, leaving itself alone in the world on a calendar nobody else could read. To retreat, it had to put back the day it had removed in 1700. Since 1712 was already a leap year, Sweden added a second one. 30 February 1712 is the only 30 February in recorded history. The year had 367 days, and real people used the date: a couple married in Ystad that day and could never celebrate the anniversary again.
Manila, 1844. The Philippines was doing something different from all of the above. It was not correcting a drift; it was crossing the International Date Line. Because of Magellan's westward voyage and three centuries of uncorrected ships' logs, the colony had been a day behind its Asian neighbours since 1521. On 16 August 1844 the Governor-General decreed that Tuesday 31 December 1844 would be deleted. Monday 30 December was followed by Wednesday 1 January 1845.
Notice what Manila lost that Rome kept. Because the correction was a date-line crossing rather than a drift, the Philippines skipped a weekday as well as a date. There was no Tuesday that week.
Alaska, 1867. The strangest of the lot. When the United States bought Alaska from Russia, the territory had to change both calendar and date line at once. Friday 6 October was followed by Friday 18 October — a jump of twelve days that landed on the same weekday it started on.