It’s older than you’ve been told!
The present Feast, commemorating the Nativity in the flesh of our Lord Jesus Christ, was established by the Church. Its origin goes back to the time of the Apostles.
In the Apostolic Constitutions (Section 3, 13) it says,
“Brethren, observe the feastdays; and first of all the Birth of Christ, which you are to celebrate on the twenty-fifth day of the ninth month.”
In another place it also says,
“Celebrate the day of the Nativity of Christ, on which unseen grace is given man by the birth of the Word of God from the Virgin Mary for the salvation of the world.”