It is almost impossible to be a Christian at this time of year without hearing about the fact that Jesus probably wasn't born on or even anywhere near December 25th, and that Christmas was just a pagan winter festival that was absorbed into Christianity. This, by the way, is completely true. While some have hypothesized that Jesus was born in the early springtime, in reality we have absolutely no idea. The Biblical account does not see fit to share it, and what clues it does provide are inconclusive at best. It is fair, then, to say that Christmas is, at least to an extent, "borrowed" from the Roman religion. However, this was far from an arbitrary decision. It has been argued that this was done to make Christianity more accessible to many Romans at the time (they wouldn't need to abandon their festivals, merely change the focus), and while I don't disagree with that statement, it's not the focus that I want to take.
December 25th was, in the Julian calendar, the Winter Solstice, hence its prominence in ancient Roman religion. Early Christians selected this date for Christmas because of the inherent symbolism: The Winter Solstice is the shortest day of the year. Every day after the Solstice, days become longer and longer, until the Summer Solstice, the longest day of the year. In other words, Christmas is the celebration of the triumph of light and the receding of darkness. December 25th symbolizes the core of Christianity: A God who loved the world to the point that He came down as a human, and that this event - called the incarnation - represents the end of sin and darkness' reign over the earth. From the moment Christ was born, the proverbial days have been getting longer, and the nights shorter. Hope is stirring.
This is a part of the reason why December 25th was chosen as the day to celebrate Christ. As a result, when we as Christians begin to ponder the question "Why do we celebrate Christmas on December 25th instead of something closer to when we think Christ was actually born?" an answer is that it's a reminder. It pushes us to take a step back and reflect on what Christmas means to the Christian: The arrival of hope and the ultimate triumph of light over darkness, grace over sin, and love over hatred. Though the night persists, and we falter, we rejoice in its inevitable demise, and the promise of Christ's return.
(As an aside, the Summer Solstice, the longest day of the year, is the Feast of St. John, or the celebration of John the Baptist. Just as how John the Baptist heralded the coming of Christ, so too does the Summer Solstice herald the coming of eternal light).
"And there will no longer be any night; and they will not have need of the light of a lamp nor the light of the sun, because the Lord God will illumine them; and they will reign forever and ever." - Revelation 22:5