A few years ago one of Daisy's not-so-bright friends saw this photo, and since she failed miserably to convert me to Christianity (that's another story though), she angrily asked why we (I'm Agnostic, Daisy is Buddhist) celebrated Christmas if we didn't believe in Jesus. Unlike Easter, Christmas' name doesn't come from a pagan goddess, but the center figure of Christianity. But Christmas' roots (especially the Western concept) are far from Christian.
Many Christians advocate putting the "Christ" back in Christmas, which goes to show why Christmas can be a religious and secular holiday. The only real major Christmas tradition (outside of music) that is really based on the story of Jesus is nativity scenes. Gift-giving, Christmas trees, and other stuff was based on pagan holidays. The most notable being the Yuletide, which merged with Christmas when the religion came to the region.
Pretty much all the pagan celebrations that merged with Christmas were from winter festivals. I don't really blame ancient Christians for keeping some of the ideas of the past. They're pretty fun traditions, which is one of the reasons why Christmas is still celebrated by those who no longer are part of the faith. It's pretty much the same logic in a different era.
At our recent Christmas celebration, my grandmother's deeply religious boyfriend started a prayer where he said that he hoped/wanted everyone to be Christian, and that Jesus was the only reason for the holiday. I don't mind sharing a holiday tradition, but I don't tolerate people bullying with their theology. We're all biased to our views, we often say things in anger, but we all can have a Merry Christmas if we want to.