Let me preclude the most obvious comment we might hear: "It doesn't really matter what day of the year Jesus was born." Okay, that is a given, at least theologically.
Yet the idea that Jesus' birth is celebrated on December 25 to replace Saturnalia does, in some regards, cast dispersion on the church of that era. We certainly know paganism had its inroads, but we want to be fair in our assessments. So it has some bearing historically.
Many Bible commentators seem to not know that there is evidence that sheep were out year round in Bethlehem. Harold Hoehner in "Chronological Aspects in the Life of Christ" writes, "...the Mishnah implies that the sheep around Bethlehem were outside all year..." (p. 26). If you consider that sheep were slaughtered year round at the Temple, it is likely that the need for sheep was perennial and year round.
So, do you think December 25 has a shot at being the real day on which Jesus was born? Is it close, possible, or impossible?
According to a site that does not think one day is more likely than another, the writer summarizes the argument for a Dec. 25 date:
From Josephus we know when Zechariah’s priestly course (Abijah) was on duty in Septemberish of BC 7. 6 months later Mary was visited by Gabriel in March. 9 months later is late December-Early January.
Of course, since we cannot all agree on the exact year that Jesus was born, and since we do not know how quickly Elizabeth became pregnant, and since we do not hold the conviction that Jesus died on the same day of the year he was conceived. But, there is a logic to things, albeit the dates, etc., would need to be ideal. The thinking is Sept. 25 is when John was concevied (shortly after Zechariah finished his duty at the Temple). Elizabeth was exactly six months along (Luke 1:26) when the angel appeared to Mary, which would bring us to March 25, and Mary conceived when the angel appeared to her. Exactly 9 months later, she gave birth to Jesus on December 25. Jesus also died on March 25.
So there is a logic there. Of course the Luke passage says "in the sixth month," which doesn't necessarily mean "at six months."
So what is your view?