First of all no one know when your Christ was born. No mention of this being a Christian holiday until Constantine. Paganism predates Christianity, and whether you like it or not. Is borrowed from pagan customs. The winter solstice or Yule, is a celebration in the rebirth of the Sun, not the son. Many Christian customs and rituals are borrowed or stolen from paganism including this holiday.
Christmas is Yule, which is a pagan holiday not just celebrated my Christians; who shouldn't really celebrate it either. If you search you will clearly find out (from the bible and many other discussions) that Jesus was not born on December 25th. December 25th is a pagan time that Christians adapted to Jesus's fake birthday.
The assumption that December 25 has absolutely anything to do with Jesus's birth is ridiculous. If you believe that Christmas is a Christian holiday, please cite a biblical passage outlining its importance. Christmas was a response by Christians to pagan holiday customs during the Winter Solstice centuries ago. Customs such as the tree, gift-giving, and many others were in place long before Christmas was established.
The origins of not only Christmas symbols but Christmas its self are pagan. According to Simple To Remember.com Judaism Online, Christmas in Christianity originated in the 4th century CE by way of Christians incorporating the pagan festival Saturnalia, which was celebrated between December 17- 25. Christians incorporated Saturnalia in an attempt to convert pagans to Christianity as pagans were ensured they could continue celebrating Saturnalia as Christians. The Christmas tree, mistletoe, presents, and Santa Clause all originated from paganism.
Christmas - literally Christ Mass - was founded to celebrate and recognize Jesus's birth. The celebration was organized to take place on a pagan holiday to celebrate feast and thanksgiving. Since this was already a popular holiday, it made sense to change this holiday into something recognized by the Christian world instead.
Originally, the word "pagan" referred to rural people, but it came to be a synonym for "non-Christian" because Christianity was primarily an urban phenomenon. So anything that is Christian is not pagan by definition. Since Christmas is a celebration of the birth of Christ, it is not a pagan celebration. Granted, it is celebrated on the same day as other pagan celebration, but that does not make it identical to those pagan celebrations.
While there are pagan symbols of Christmas such as Santa Claus and Rudolph, the holiday is a celebration of the birth of Christ. Christmastime is also a season when many people are especially loving and kind, and take special care to help those in need, which is a Christian principle, although individuals of other religions believe in this ideal as well.
Christmas celebrates the birth of Jesus Christ, and is a Christian holiday. The timing is the same as the Winter Solstice, which is a pagan holiday, but the two are very different. Early Christians incorporated some of the traditions from various pagan holidays into Christmas, to make it more palatable to non-Christians of the time. However, that doesn't change the meaning or reason for the Holiday.
Christmas takes hints and roots from many pagan traditions, from the tree and its ornaments to Santa Claus to its date near the winter solstice, but it has certainly become its own event across the years. Christians certainly have their own traditions around the holiday, and so it can be a Christian holiday. Secular people have plenty of their own traditions to follow on Christmas as well, so it doesn't even have to be about religion.