In the early 1900s, a group of conservative Christians banded together to protect the "fundamentals" of our faith from the liberal theology which tried to get rid of them. These men and women of God rallied together around five key points: the virgin birth of Christ, substitutionary atonement (Christ died in our place), the inerrancy of Scripture, the divinity of Jesus (that he was fully God), and (taken together) the bodily resurrection of Jesus and his future Second Coming. As more and more theologians and churches left these doctrines behind, the Fundamentalists sought to preserve them as essential to biblical Christianity.
It's easy to spot which of the fundamentals relates to Christmas: the virgin birth of Jesus. While liberal denominations either don't care about Mary's virginity or try to refute it entirely, most Bible-believing Christians take it seriously. If Jesus were Joseph's son (or another man's, for that matter), how could he be the Son of God? At best God would have to adopt him somehow (a view soundly rejected throughout church history); at worst Jesus was a lunatic and a liar.
People who don't believe in the virgin birth actually cite the prophecy about it from Isaiah 7:14: "Therefore the Lord himself will give you a sign: the virgin will conceive and give birth to a son, and will call him Immanuel." The word for "Virgin" can also be taken as "young woman," so people say, "Isaiah just says a young woman will conceive. Big deal." But no one in 2,000 years has seriously taken this verse that way. No one working in any language ever thought a simple, ordinary birth would be a miraculous sign from God that His Son is now with them -- is Immanuel, "God with us."
As we celebrate Christmas in the weeks ahead, think back on the Virgin Mary, her fear and surprise that she would give birth without knowing a man (Luke 1:26-38). Believe Jesus is truly God with us, the only begotten Son of the Father, conceived by the Holy Spirit. Only a man who is also God could come on Christmas to die for our sins at Easter. Only Jesus is the prophesied Savior.