I saw this article supporting the usual date among Christians:
The date can be derived historically from the dating of Zechariah’s entry into the temple to burn incense. It can also be derived theologically from the ancient tradition that a great prophet entered and left the world on the same calendar day. Thus, the Annunciation was determined to have occurred on the same day as the crucifixion, March 25. December 25 naturally follows nine months later. They are good arguments, held to strict standards of historical research and logic, within their own fields.
Biological evidence that Jesus actually was born in December
Rebecca Salazar | Dec 10, 2017
Now, to this can be added, the Awassi sheep she mentions.
But here is one more, and it has some theological bearing on whether we should celebrate a birthday in the case of Christ or not.
I find it very probable that on the exact date of Christ's being 30 years old, He rejected Satan's birthday presents - and, being exhausted physically after so doing, accepted those of a good angel.
There is a Hebrew tradition of not celebrating birthdays. It is not breaking a Mosaic law, but it is breaking a Pharisaic tradition to celebrate a birthday. This tradition has been kept up by Catholics, through the Middle Ages and even beyond in some conservative regions : you celebrate your baptismal date, not your birthdate.
There is a theological reason why only 3 birthdays are Church holidays : the Blessed Virgin and Our Lord were born without original sin and also conceived without it, St John the Baptist was conceived with but born without original sin (delivered from it when the Blessed Virgin visited St Elisabeth). There are perhaps two more birthdays (Isaiah and Jeremiah) which the Church could celebrate for a similar reason.
But there was also a pragmatic reason in preparing our salvation in the late OT aversion against Birthdays : Satan's offer was so to speak a "birthday present". And it is the kind of thing Christians do not give each other for either Christmas or birthday presents, normally : power.
The angel came and gave Christ unexpected, indeed "miraculous" (as when the raven fed Elijah) food. And food is a Christmas present and birthday present which is acceptable. Even, food and drink - probably wine (whiskey was not invented and besides wine better fits the Holy Land). Water, He probably had drunk, so his survival for forty days was not in that sense miraculous.
How do I figure out this is indeed the date, probably?
Baptism of Christ, before fasting and temptation:
"Luke 3: And Jesus himself was beginning about the age of thirty years;"
Marriage at Cana: Our Lord was probably some days past thirty, since the Pharisaic tradition allowed for a party after the thirtieth birthday (according to a reference I am not now finding) - or other important birthday - where someone is acknowledged as being of age.
This brings us to the question whether January 6 was the actual date of baptism, or of marriage at Cana - it is celebrated as both, as well as visit of the Magi (and in some traditions in the place of Christmas too).
Now, since marriage at Cana was about 40 days after baptism, or perhaps a bit more, celebrating both events on same day means you are actually taking one of them away from actual date. I propose January 6 is "more like" marriage of Cana, and Our Lord was then baptised before November 27th.*
And, this is a space in which December 25th falls near the end. Between that day and January 6th, Christ had the opportunity to gather some disciples, as the situation of the marriage at Cana implies.
I checked on Jewish Holidays for 1999 to 2050. The earliest dates for first day of Hanukkah are just after that day : 28, 29, 30 November. Either Christ's baptism was on an early Hanukkah (fitting enough, since His body is among human bodies the primary Temple of the Holy Ghost) or He celebrated Hanukkah in the desert; fasting, preparing the rededication which was greater than that in 164 BC.
It is possible for Hanukkah to fall as late as December 25 or even a few days later.
But this said, the other enumeration of reasons, cited, is good too, and more precise, and now read Rebecca Salazar's evidence on the sheep specific to the region. The Awassi sheep.
Hans Georg Lundahl
Holy Thirty Martyrs
of Via Lavicana, between two Laurels**
* 6.I="37.XII"="67.XI", 67 - 40 = 27. ** Romae, via Lavicana, inter duas Lauros, natalis sanctorum triginta Martyrum, qui omnes una die, in persecutione Diocletiani, martyrio coronati sunt.