I don't know about the May 21 bit, but December 21st is the Winter Solstice. Older civilizations like the Celts, the Aztecs, etc., who used the movements of the sun and moon to keep track of the seasons and years tended to use this, the shortest day of the year, as one of the 'benchmarks' to anchor the calendar. At this time, the sun was lowest in the sky at noon, and rose the furthest north of true east. There are many myths that refer to this as the day when the Sun starts its journey back from death. The 'rebirth' of the Sun is also the reason that the Christian churches set the festival of Christ's birth in December - the Bible refers to shepherds sitting out with their flocks at night, which doesn't happen in mid-winter. Any historical Christ (and I don't dis-count that there may have been one) would have been born in spring or summer by that description.