We do want to honor Christ, and try to do it by following His example (John 12:26; 1 John 2:6) and doing what He said—obeying His commands (Luke 6:46; John 14:15).
Example of Christ and the New Testament Church. Jesus Christ and the early New Testament Church didn't celebrate Christmas. There is no command to celebrate Christ's birthday, and in fact there is no mention in the Bible of the Church ever celebrating it. The Bible doesn't even tell us when He was born, but it is clear from Scripture that it couldn't have been Dec. 25. The Interpreter's One-Volume Commentary explains that Luke 2:7-8 argues "against the birth [of Christ] occurring on Dec. 25 since the weather would not have permitted" shepherds watching over their flocks in the fields at night. Also, the Roman census (Luke 2:1-4) would not have been taken in winter, when temperatures often dropped below freezing and roads were in poor condition.
History. "The tradition of celebrating December 25 as Christ's birthday came to the Romans from Persia. Mithra, the Persian god of light and sacred contracts, was [supposedly] born out of a rock on December 25. Rome was famous for its flirtations with strange gods and cults, and in the third century  the unchristian emperor Aurelian established the festival of Dies Invicti Solis, the Day of the Invincible Sun, on December 25...
"[Emperor Constantine] was probably instrumental in seeing that the major feast of his old religion was carried over to his new faith" (Gerard and Patricia Del Re, The Christmas Almanac, 1979, p. 17).
Pagan winter holidays were renamed for Christ to make it easier for pagans to become Christian, but many of their old customs used to worship false gods remained.
God's commands. The Bible has much to say about trying to honor God in the way others worshipped their "gods" (Deuteronomy 12:30-32) or according to the commands and traditions of men (Matthew 15:8-9).
Though Jesus did not tell us to celebrate His birth, He did leave clear instructions about how to commemorate His death (1 Corinthians 11:23-26) and other festivals kept by the early Church (John 7:1-2, 10; Acts 2:1; 18:21; 20:6, 16; 27:9; 1 Corinthians 5:6-8; etc.; compare Leviticus 23).
For More Information, request our free booklets Holidays or Holy Days: Does It Matter Which Days We Keep? and Jesus Christ: The Real Story (www.ucg.org).