Why does the church celebrate Jesus’ birth on December 25th?
The short answer is, Jesus wasn’t necessarily born on December 25th (see this article for more), but this was an early tradition of the church which has been maintained until today.
The evidence suggests that there was interest in calculating the date of Jesus’ birth in the early church but at first there was no clarity or unanimity about it.
For example, around the year A.D. 200, in a work titled Stromata, Clement of Alexandria gave his calculation that Jesus was born on November 17 or 18 based on his reckoning of how long before the death of Emperor Commodus Jesus’ birth occurred. However, he noted that others had differing opinions: “There are those who have calculated not only the year of our Lord’s birth, but also the day. They say that it took place in the twenty-eighth year of Augustus, on the twenty-fifth day of Pachon [May 20] … Others say that He was born on the twenty-fourth or twenty-fifth day of Pharmuthi [April 19 or 20].” He also mentions that the followers of Basilides believed Jesus was born on January 10 or January 6.
Others argued for a December birth based on the belief that Jesus was conceived in March (sometimes this also connected with the date of his death).
“The evidence suggests that there was interest in calculating the date of Jesus’ birth in the early church but at first there was no clarity or unanimity about it.”
Around the same time as Clement, another church leader named Julius Africanus wrote a detailed chronology of the entire world. Only a few fragments of this work are still available, but it shows he calculated that Jesus was conceived on March 25 and thus born nine months later in December.
Around A.D. 205, the church father Hippolytus wrote a commentary on Daniel. He reached the same conclusion as Julius based on his understanding of the 70 weeks prophecy in Daniel 9. He wrote:
“For the first advent of our Lord in the flesh, when He was born in Bethlehem, was eight days before the Kalends of January [i.e., December 25], the fourth day [Wednesday], while Augustus was in his forty-second year.…He suffered in the thirty-third year, eight days before the Kalends of March [March 25], the day of preparation, the eighteenth year of Tiberius Caesar.”
Early church leaders explored this matter out of historical and theological interest, but there was little in the way of any church celebration of Jesus’ birth.
“Early church leaders explored this matter out of historical and theological interest, but there was little in the way of any church celebration of Jesus’ birth.”
Over the next several decades, however, December 25 eventually became the accepted date for the birth of Jesus in the Western church (the East connected it with the Feast of Epiphany on January 6). This date became so widely held that by the time of Augustine (c. A.D. 400) he could simply say that this is when it was believed Jesus was born.
“For He is believed to have been conceived on the 25th of March, upon which day also He suffered; so the womb of the Virgin, in which He was conceived, where no one of mortals was begotten, corresponds to the new grave in which He was buried, wherein was never man laid, neither before nor since. But He was born, according to tradition, upon December 25th.” 
So, December 25th became the established tradition in the church.
One popular criticism of December 25th celebrations of Jesus’ birth is that it was borrowed from pagan holidays. One of the common ways this is expressed is that December 25th was celebrated as a Sun festival in the Roman Empire (Sol Invictus) and Christians appropriated that as the birthday of Jesus.
“One popular criticism of December 25th celebrations of Jesus’ birth is that it was borrowed from pagan holidays.”
Before evaluating this claim, it’s important to note that even if early Christians replaced a pagan holiday with a celebration of Jesus’ birth, that would not in and of itself make Christmas pagan. What is celebrated and how it is celebrated matter far more than date it is celebrated. Displacing a pagan holiday by celebrating the birth of the world’s true King would be a triumph of the gospel not a capitulation to culture.
Nevertheless, the brief survey above shows the error of the notion that Christmas comes from a pagan holiday. We see that the early Christians began associating Jesus’ birth with December 25th quite early, well before they had any control over the Imperial calendar. And they did so for reasons completely unrelated to displacing a Sun festival.
Not only that, but as best as we can tell, Sol Invictus didn’t rise to any sort of prominence in the Empire until Emperor Aurelian built a new temple for the sun in A.D. 274. Coincidentally, he did dedicate his new temple on December 25, but Christians had already been suggesting that date for the birth of Jesus for at least 74 years. Perhaps Aurelian’s aim in dedicating it on that day was to diminish the increasing influence of Christianity which by his time was quickly taking over as the dominant religion in the Empire? At any rate, even though he dedicated his new temple on that date, there is no certain evidence of any Sun festival associated with December 25th until much later.
“We see that the early Christians began associating Jesus’ birth with December 25th quite early, well before they had any control over the Imperial calendar.”
In an infographic available online, Wes Huff explains that “Sol Invictus was not placed on 12/25 until 354 AD when the Philocalian Calendar records this but doesn’t specify any festival with regards to sun worship. Prior to this, the Julio-Claudian fasti inscriptions say Sun festivals were on August 8th, 9th, 28th, and December 11th. The Philocalian calendar says emperor Aurelian honoured the sun with chariot races every 4 years Oct 19-22.”
So although the claim that Christians co-opted a pagan holiday is easy to find on the internet, it is not based on history.
So why do we celebrate Christmas on December 25? Simply because that date rose to the top among early Christians as the date for the birth of Jesus. As the church spread to the West, the tradition of honoring Christ’s birth on December 25 spread with it.
For more from John, see his website and Listener’s Bible Commentary.