Pro 16:25 There is a way that seemeth right unto
a man, but the end thereof [are] the ways of death.
There is no command, directive, statute, law, or precept for
Christians to celebrate Christmas. Pagan origins for the date and customs of Christmas can easily be found in an encyclopedia or the Internet. I do not need to add to them. The history of Christians who also did not celebrate Christmas can be found as well. Simply though, we were not commanded to observe that day.
There are commands for the children of God in the New Testament to observe though. If we believe on Christ, we are told to be baptized (Mark 16:16, Acts 2:38). Another ordinance for Christians to remember is the Lord's Supper (Matt 26:26; 1 Cor 11:24, 25). These were given as acts of worship and service toward God specifically mentioned in the New Testament.
To serve God in ways we were not directed to by the Bible is forbidden, especially when those observances are of heathen origin:
(Deut 12:29-30, 31)
When the LORD thy God shall cut off the nations from before thee,
whither thou goest to possess them, and thou succeedest them, and
dwellest in their land;
Take heed to thyself that thou be not snared by following them, after
that they be destroyed from before thee; and that thou enquire not
after their gods, saying, How did these nations serve their gods? even
so will I do likewise.
Thou shalt not do so unto the LORD thy God:...Jeremiah deals with this too: (Jeremiah 10:2)
Thus saith the LORD, Learn not the way of the heathen, and be not dismayed at the signs of heaven; for the heathen are dismayed at them.
Now wait. How many things have we learned from the "heathen" (unbelievers)? We all drive cars, Christian or not. We use the same language as unbelievers, in this case English. We seek to make a living with our jobs just like unbelievers. (Of course, there is a difference in the way we conduct ourselves in each of these catagories but I digress.) If you read the rest of Jeremiah 10, you will see clearly that we are not to learn the practices unbelievers use to serve their gods.
Finally, there is an example in Scripture of people using pagan symbols and practices to serve the "Lord":
(Ex 32:4, 5)
And he received [them] at their hand, and fashioned it with a graving
tool, after he had made it a molten calf: and they said, These [be] thy
gods, O Israel, which brought thee up out of the land of Egypt.
And when Aaron saw [it], he built an altar before it; and Aaron made proclamation, and said, To morrow [is] a feast to the LORD.
Can you believe it? This was "a feast to the LORD." Read Exodus 32 for the complete story of the golden calf.
These are the reasons that I do not celebrate Christmas. I do not expect to convince anybody, though it might be nice :) Entire books have been written on this subject but what I have written is the summary of what I believe.