But the calculation of the birth of Jesus was doubly inaccurate. On one hand, Herod the Great died in 4BC, which would bring the end of the millennium back to 24 December 1996. On the other hand, the census in Judaea was held in 6AD, which would take it forward to 24 December 2005. Moreover, earlier Christians preferred spring to winter as the season of the Nativity. So there is no way of knowing when it occurred, if it did.
If there is no certain date for the beginning of the first millennium, there is no correct date for the end of the second one. Anyway, whatever date might make logical sense, virtually everyone will choose 31 December 1999 because it comes earlier and because most people prefer the look of numbers to their meaning.