Nobody knows when He was born
Nobody really knows when Jesus was born. We know it can't be December 25th because of the shepherds, but in John's gospel it says "the Word was made flesh and "dwelt" among us. The word that the KJV translates as dwelt is a Greek transliteration of the Hebrew word tabernacle. The word tabernacle first appears in the book of Exodus in conjunction with the Hebrew feast of tabernacles when the Jews dwell in tents to commemorate the forty years in the wilderness, during which time they actually dwelt in tents.
There were a lot of other Greek words for dwell around at John's time yet He chose this one, why? Maybe because Christ was born during this feast.
The Feast of Tabernacles is celebrated in late September early October by our calendar. Now if we count back nine months from that time of year we wind up in late December early January, so if Christ was conceived around that time December 25th is a perfectly good day to celebrate His entry into the world.