Scholars are still discussing the dating of Jesus' birth. These are the most common arguments:
Picking a Month and Day - Traditional Approaches
Tradition holds that Jesus was born on December 25. The popular notion is that the Catholic Church picked December 25th because it was a very popular Roman festival – the celebration of Saturnalia. This weeklong festival celebrated the birth "the Unconquerable Sun God" and was known for merriment and drunkenness. Gifts were exchanged on the 24th and the weeklong celebration ended with Saturnalia's birthday on the 25th. Christians supposedly chose the 25th to appease newly converted pagans who were reluctant to give up their festivals.
Another possibility derives more from Judaism, and involves linking Jesus' birth to the date of his death. Around 200 CE, scholars determined that Jesus was crucified on March 25th, exactly nine months before December 25th. At some point, March 25th became known as the Feast of the Annunciation – the date when Jesus was conceived. The whole notion of his conception and death occurring on the same date conflates ideas of creation, redemption, and salvation. Others agreed with this idea, but instead of using the Hebrew calendar, they calculated it off the Greco-Roman calendar and came up with a birth date of January 6th.
Picking a Month and Day - Scholarly Approaches
However, modern scholars point to the Biblical record and challenge these dates. According to Matthew, shepherds were in attendance at the birth. Palestinian sheepherders would take their sheep out shortly after Passover, which is in the spring, and bring them inside early in October or November. Thus, it is unlikely that there would be shepherds "abiding in the fields with their flocks" on December 25th – it would have been too cold. On that basis, modern scholars argue for a time between May and September. In addition, some scholars think the presence of lambs in the story suggests Jesus was born in the spring, since that is when lambs are around.
Scholars have also used the priestly rotation that was established by David in Leviticus and 1 Chronicles to calculate Jesus' birthday. We know that John the Baptist's father Zechariah was the head priest shortly before John was conceived and that Zechariah's term would have occurred in May/June. Thus, John the Baptist was conceived shortly after that, and, according to Luke, Jesus was conceived within 6 months. That puts Jesus' conception in December and his birth in September.
Since both Matthew and Luke tell us that Jesus was born while Herod was king and scholars know that Herod died in 4 BCE, Jesus' birth must have been before 4BCE. In addition, scholars know that Cyrenius (also known as Quirinius), who administered the tax references in Luke 2:2, became governor of Syria in 6 BCE. Based on this evidence, Jesus was most likely born between 6 and 4 BCE.
Some scholars have recently noted that there were two actually governors with the name of Cyrenius. This fact might allow for an earlier dating (perhaps before 10 BCE), but most scholars still think between 6 and 4 BCE is the most likely scenario.
Interestingly, there is nothing in the New Testament that suggests the authors of the Gospels had any interest in the date of Jesus' birth. However, by 200 CE several apocryphal writings had expanded on information about his birth and childhood, and interest in the date was a natural progression. But December 25th is not mentioned in any of these writings. In fact, most mention April or May. By the fourth century, however, there are several references to either December 25th or January 6th, based on the above information.
The bottom line is that scholars really don't know.