Dec. 25th. The date of the birth of Jesus Christ.

Here are  a few sources for the traditional date of the Birth of Jesus

Dom Gueranger, The Liturgical Year

https://tinyurl.com/4468ssr4

Alfred Edersheim, in his "The Life and Times of Jesus"

And yet Jewish tradition may here prove both illustrative and helpful. That the Messiah was to be born in Bethlehem, was a settled conviction. Equally so, was the belief , that He was to be revealed from Migdal Eder, 'the tower of the flock.' This Migdal Eder was not the watchtower for the ordinary flocks which pastured on the barren sheepground beyond Bethlehem, but lay close to the town, on the road to Jerusalem. A passage in the Mishnah [951] leads to the conclusion, that the flocks, which pastured there, were destined for Temple-sacrifices [952], and, accordingly, that the shepherds, who watched over them, were not ordinary shepherds. The latter were under the ban of Rabbinism, on account of their necessary isolation from religious ordinances, and their manner of life, which rendered strict legal observance unlikely, if not absolutely impossible. The same Mishnaic passage also leads us to infer, that these flocks lay out all the year round, since they are spoken of as in the fields thirty days before the Passover -- that is, in the month of February, when in Palestine the average rainfall is nearly greatest. 

Thus, Jewish tradition in some dim manner apprehended the first revelation of the Messiah from that Migdal Eder, where shepherds watched the Temple-flocks all the year round. Of the deep symbolic significance of such a coincidence, it is needless to speak. 

It was, then, on that ‘wintry night’ of the 25th of December, that shepherds watched the flocks destined for sacrificial services, in the very place consecrated by tradition as that where the Messiah was to be first revealed. 

https://taylormarshall.com/2012/12/yes-christ-was-really-born-on-december.html