The question about the actual birthdate of Jesus of Nazareth is quite debatable. While few probably give it much serious thought, it seems that the most common assumption, at least in my circles, among those who do think about such things, is that it has to be at almost any time of year other than late December. I certainly do not have a definitive answer. I can’t say I even have a firm opinion. But I am at least intrigued by the suggestion of historian Alfred Edersheim, in his classic tome, The Life & Times of Jesus the Messiah, in which he makes a case for the traditional December 25 date:

So much, that is generally accessible, has of late been written on this subject, and such accord exists on the general question, that only the briefest statement seems requisite in this place, the space at our command being necessarily reserved for subjects which have either not been treated of by previous writers, or in a manner or form that seemed to make a fresh investigation desirable.

At the outset it must be admitted, that absolute certainty is impossible as to the exact date of Christ’s Nativity – the precise year even, and still more the month and the day. But in regard to the year, we possess such data as to invest it with such probability, as almost to amount to certainty.

1. The first and most certain date is that of the death of Herod the Great. Our Lord was born before the death of Herod, and, as we judge from the Gospel-history, very shortly before that event. Now the year of Herod’s death has been ascertained with, we may say, absolute certainty, as shortly before the Passover of the year 750 A.U.C., which corresponds to about the 12th of April of the year 4 before Christ, according to our common reckoning. More particularly, shortly before the death of Herod there was a lunar eclipse (Jos. Ant. xvii.6.4), which, it is astronomically ascertained, occurred on the night from the 12th to the 13th of March of the year 4 before Christ. Thus the death of Herod must have taken place between the 12th of March and the 12th of April – or, say, about the end of March (comp. Ant. xvii.8.1). Again, the Gospel-history necessitates an interval of, at the least, seven or eight weeks before that date for the birth of Christ (we have to insert the purification of the Virgin – at the earliest, six weeks after the Birth – The Visit of the Magi, and the murder of the children at Bethlehem, and, at any rate, some days more before the death of Herod). Thus the Birth of Christ could not have possibly occurred after the beginning of February 4 b.c., and most likely several weeks earlier. This brings us close to the ecclesiastical date, the 25th of December, in confirmation of which we refer to what has been stated in vol. i. p.187, see especially note 3. At any rate, the often repeated, but very superficial objection, as to the impossibility of shepherds tending flocks in the open at that season, must now be dismissed as utterly untenable, not only for the reasons stated in vol. i. p.187, but even for this, that if the question is to be decided on the ground of rain-fall, the probabilities are in favor of December as compared with February – later than which it is impossible to place the birth of Christ.

2. No certain inference can, of course, be drawn from the appearance of the star’ that guided the Magi. That, and on what grounds, our investigations have pointed to a confirmation of the date of the Nativity, as given above, has been fully explained in vol. i. ch. vi… (see specially p.213).

3. On the taxing of Quirinius, see vol. i. pp.181, 182.

4. The next historical datum furnished by the Gospels is that of the beginning of St. John the Baptist’s ministry, which, according to St. Luke, was in the fifteenth year of Tiberius, and when Jesus was about thirty years old’ (St. Luke iii.23). The accord of this with our reckoning of the date of the Nativity has been shown in vol. i. p.264.

5. A similar conclusion would be reached by following the somewhat vague and general indication furnished in St. John ii.20.

6. Lastly, we reach the same goal if we follow the historically somewhat uncertain guidance of the date of the Birth of the Baptist, as furnished in this notice (St. Luke i.5) of his annunication to his father, that Zacharias officiated in the Temple as on of the course of Abia’ (see here vol. i. p.135). In Taan.29 a we have the notice, with which that of Josephus agrees (War vi.4.1.5), that at the time of the destruction of the Temple the course of Jehoiarib,’ which was the first of the priestly courses, was on duty. That was on the 9-10 Ab of the year 823 A.U.C., or the 5th August of the year 70 of our era. If this calculation be correct (of which, however, we cannot feel quite sure), then counting the courses’ of priests backwards, the course of Abia would, in the year 748 A.U.C. (the year before the birth of Christ) have been on duty from the 2nd to the 9th of October. This also would place the birth of Christ in the end of December of the following year (749), taking the expression sixth month’ in St. Luke i.26, 36, in the sense of the running month (from the 5th to the 6th month, comp. St. Luke i.24). But we repeat that absolute reliance cannot be placed on such calculations, at least so far as regards month and day. (Comp. here generally Wieseler, Synopse, and his Beiträge.)

Source: Appendix vii, The Life & Times of Jesus the Messiah