You beat me to it.
And Docetboy, it is quite true there (1) there is no biblical evidence for what time of year Jesus was born (except that it was probably late spring, summer or early fall, since "there were shepherds abiding in the fields, keeping watch over their flock by night," and it would have been too cold for that in the winter) and (2) the monks who estimated the birth of Jesus were off by a few years.
But it probably isn't that accurate to suggest it was just a matter of instituting the celebration of the birthday of Jesus to replace a pagan festival. While what Mario Righetti "candidly admits" has some truth to it, it really doesn't reflect the full history.
It is commonly put forth that Christmas (remember, that is just the English name -- other languages use words related to birth, incarnation, pagan-rooted names like "Yule" or something like the German "Holy Night") is the birthday of Christ, but as far as the Church has historically been concerned, that is something of a surface understanding. What Christmas really is, again as far as the teaching of the Church has gone, is the festival of the Incarnation -- that is, the celebration of the doctrine that God became human through the birth of Jesus. Christians would say this is a true miracle, one of the 2 biggest ever. With Easter, Christmas on the surface celebrates a historical event, but on a deeper level these two holidays celebrate the two cornerstone beliefs of Christianity: the Incarnation and the Resurrection.
In early centuries, the Church in various places chose various times of year to specifically celebrate the doctrine of the Incarnation. In some parts of the East, a January observation became popular. The Church in Rome did indeed adopt and adapt the pagan celebration of the Invincible Sun, partly because of the belief that it would be an easy transition for pagans to make, but also because the winter solstice themes of the Festival of the Invisible Sun -- light coming into and defeating the darkness -- were quite apt for celebration of the Incarnation and resonated with some of the biblical passages concerning the Incarnation, especially from the Gospel of John.
Rome's celebration eventually became the norm throughout the Christian world, although the Eastern January celebration survives in the celebration of Epiphany (the 12 days from Christmas to Epiphany being the 12 days of Christmas). The fact that most cultures have winter solstice festival of some sort (there's a reason Hanukkah -- the Festival of Lights -- comes at this time of year) supported the adoption of December 25, since it made transition from pagan to Christian easier. The Church in the first millenium was rarely hesitant to adapt the pagan customs it could and infuse them with different meaning.
So there is indeed no biblical directive to celebrate the birth of Jesus (or Easter for that matter, although there is biblical evidence for Christian observation of Sunday rather than the Sabbath). And clearly, pagan celebrations played into the choice of dates for Christmas. But (from a Christian perspective), there is ample basis for the Church designating a time to devote to specific celebration of the miracle of the Incarnation, and experience has shown that the date chosen has supported the meaning of the observance quite well.
Sorry for the long-windedness. My son and I had this very discussion last night, when he asked why we celebrate Christmas on December 25 when we don't know when Jesus was born.