The Bible does not command Christians to celebrate Christmas. This is entirely true. Christians are not obligated by the scriptures to celebrate Christmas (or any other holidays, for that matter). On the other hand, Christians are not forbidden to celebrate key events in the life of Jesus and the beginnings of the church. Thus, Christian believers are free to celebrate or to not celebrate, provided they do not try to impose their choices on other believers. The value of either is not in the choice made, but in the heart of the one choosing. I'll return to that shortly.
Christmas is a Pagan Holiday! Christmas is a Romish Holiday! Christmas trees are really idols! Puh-lease! Taking the second objection first (and speaking as a Protestant), this isn't the 16 or 17 century! However awful the Catholic Church may have been then – and many Protestants' hands back then were far from squeaky clean! - that is not the Catholic Church of today. Those battles of the 16th, 17th, and 18th Centuries have been extinguished by time and learning born out of suffering. More importantly, there are many true believers in Jesus among Catholics.
Regarding the claim concerning Christmas trees, Jeremiah 10:2-5 is commonly cited:
Thus says the LORD: "Learn not the way of the nations, nor be dismayed at the signs of the heavens because the nations are dismayed at them, for the customs of the peoples are vanity. A tree from the forest is cut down and worked with an axe by the hands of a craftsman. They decorate it with silver and gold; they fasten it with hammer and nails so that it cannot move. Their idols are like scarecrows in a cucumber field, and they cannot speak; they have to be carried, for they cannot walk. Do not be afraid of them, for they cannot do evil, neither is it in them to do good."
While the Hebrew text does not use the word “idol,” it is clear that this text mockingly describes the making and worshiping of an idol: “worked with an axe by the hands of a craftsman;” “decorate it with silver and gold;” “they have to be carried .” Christmas trees are, of course, usually cut down from a forest, but are not worked by a craftsman, as idols were. Christmas trees are commonly colorfully decorated, but usually not with real silver or real gold, as idols were. Christmas trees are not carried around, as idols were. More to the point, while decorating a Christmas tree is often a time of family enjoyment and togetherness, it isn't worshiped, and some time after Christmas, when it has served its seasonal (a month or two at most!) decorative purpose, it is stripped of its decorations and thrown out.
The genesis of celebrating Jesus' birth and the choosing of December 25th for that celebration were very long ago, and the reasons for the latter are obscure. It is entirely possible that Jesus was not born in December, let alone exactly on the 25th of December. But, for the sake of argument, let me stipulate that the date was chosen because it was the date of a Pagan holiday, that Jesus was born in any month but December, and that many customs – e.g. Christmas trees – have Pagan origins. So what! I can guarantee that no Christian celebrating Christmas is covertly worshiping Saturn or Odin or Thor! But here again, the value is not in the date or the trappings of the celebration.
The core of Christian life and practice is not in a list of do's and don't's. That core is in the believer's heart. When one's heart is right, i.e. there is true faith and belief, one's actions follow that heart. In the case of celebrating Christmas, it comes down to a question of what (Whom!) the person is celebrating. If Christian believers celebrating Christmas are celebrating the birth of Jesus – thanking Him, honoring God for such a priceless Gift, reflecting on what that Gift means in one's life, thinking about how that Gift affects and is shown in one's daily life – then what people 2000 years ago may or may not have done on the 25th of December, how that date came to be chosen for celebrating Christmas, or how things such as decorated trees were used 15 or 20 centuries ago really do not matter. What matters is the celebrant's (or non-celebrant's) heart.