But when you think about it, none of the existing holidays on the calendar would have been terribly important to the early followers of Jesus. They were still marching to the beat of a different drummer in the late third and early fourth centuries.
So, count nine months from March 25th and you end up at December 25th. It is no surprise, then, that the church chose to celebrate the Nativity on that day.
A related question that occasionally comes up has to do with the Russian Orthodox Church's Christmas celebration on January 7th. Several of the Eastern Orthodox churches still fix the date of Christmas using the old Julian calendar. December 25th in the Julian calendar is the same as January 7th in the newer Gregorian calendar that most of us use.
The Armenian (not Arminian, as in the 16th century Dutch theologian Jacobus Arminius, but Armenian, as in the ancient people of Armenia) Apostolic Church holds their celebration of the Nativity in combination with the Feast of the Epiphany on January 6th. There is actual ancient precedent for that practice, too. (Some of the churches which did not follow Rome too closely developed in slightly different ways. And really, the Armenian practice is not a lot different than that of many modern evangelicals who throw together the Christmas and Epiphany stories -- and do it all on December 25th -- skipping the 12 days of Christmas that culminate in the Epiphany celebration on January 6th.) To complicate matters even more, while most of the Armenian churches use the Gregorian calendar, a few use the Julian calendar. Those who are on the Julian calendar celebrate both the Nativity (Christmas) and Epiphany on January 19th (Gregorian calendar).
Did you follow all of that?
In many ways, the actual date of Christmas is relatively unimportant. To borrow an over-used phrase from pop-culture, what matters most is "the reason for the season."
In the sixth month of Elizabeth’s pregnancy, God sent the angel Gabriel to Nazareth, a village in Galilee, to a virgin named Mary. She was engaged to be married to a man named Joseph, a descendant of King David. Gabriel appeared to her and said, “Greetings, favored woman! The Lord is with you!”
Confused and disturbed, Mary tried to think what the angel could mean. “Don’t be afraid, Mary,” the angel told her, “for you have found favor with God! You will conceive and give birth to a son, and you will name him Jesus. He will be very great and will be called the Son of the Most High. The Lord God will give him the throne of his ancestor David. And he will reign over Israel forever; his Kingdom will never end!”
Mary asked the angel, “But how can this happen? I am a virgin.”
The angel replied, “The Holy Spirit will come upon you, and the power of the Most High will overshadow you. So the baby to be born will be holy, and he will be called the Son of God. What’s more, your relative Elizabeth has become pregnant in her old age! People used to say she was barren, but she’s now in her sixth month. For nothing is impossible with God.”