Because the distance between God and His creatures is so great, the only acceptable way of approaching God in worship must be revealed to us by God Himself.
Acceptable worship for the Church is prescribed through commands and examples found in Scripture.
The teaching mentioned above is called the "Regulative Principle of Worship."
I've had two friends-- one Reformed Baptist, and one Presbyterian-- who have tried to apply the Regulative Principle in such a way as to argue that Christians should not celebrate Christmas. At first I thought that they might be making a valid point in their arguments, but upon further examination I find their arguments to be almost entirely without merit.
Christmas is a national holiday. Christians are not forbidden to celebrate national holidays. Moreover, Christians-- following the example of Jesus-- are permitted to celebrate holidays instituted by people.
Jesus celebrated Purim (the feast mentioned in John 5, when one examines the chronology of John) and Hanukkah (John 10:22-24; "The Feast of the Dedication" is another name for Hanukkah), which were Jewish national holidays with religious significance that were instituted by the people after the giving of the Law was already completed. Purim is given by the Westminster Confession of Faith (a document written by theologians who were committed to the Regulative Principle) as one example of proper "thanksgivings upon special occasions."
Above, I wrote that the arguments against Christians celebrating Christmas are almost entirely without merit. The reason that I wrote "almost" is because Christians can certainly take Christmas celebrations to ungodly excess; also, churches can introduce pageantry or ceremonies in worship around Christmastime that clearly violate the Regulative Principle and distract from the gospel.
But if Christmas is truly used as a time of thanksgiving for the Incarnation, then it is an entirely appropriate holiday for Christians, who should use our society's rather superficial mentions of Christ's birth to introduce people to Jesus Himself through the proclamation of the gospel.