Contrary to popular beliefs, there's no explicit mentioning in the Bible that Jesus Christ was born on 25th December.
Many theories were proposed over the last 20 or so centuries to reconcile the fact - Isaac Newton thought the date was selected to correspond with the winter solstice. A German Protestant thought it was originally the date of the Roman solar holiday, and thus a "paganization" of the church. Some scholars tried to establish the legitimacy by using various Biblical sources, and assumptions.
Amusing that's, an elder-day theologian stated that (in the days of early Church), "only sinners who make great rejoicings over the day on which they were born into this world below."

