The first Christians were not concerned with the date of Christ’s birth nor celebrating it. Origen (d. 255), Irenaeus (d. 202), and Tertullian (d. 220) do not include Christmas or its date on their lists of feasts and celebrations.
The earliest attempts to date the birth of Christ produced various results:
c. 200 Clement of Alexandria noted that Christians in Egypt believed Jesus was born on May 20th
De paschæ computus written in 243 notes the some groups of Christians celebrated the feast of Christ’s birth on March 28 and others on April 19/20.
The writings of Theophilus (d.181) and Hippolytus (d. 240) mention Christ was born on December 25
4th and 5th century writings mention December 25 as an ancient and widespread feast of Christ’s birth
Many ancient writings, especially in the East, place the celebration on January 6 but usually combined with what we now celebrate separately with the Epiphany
The Church chose December 25th due to its ancient origin and widespread acceptance. No other date was accepted by more Christians for a longer or older period of time. However we should note that the Church chooses this date to celebrate the birth of Jesus Christ, She is not declaring that it is literally the day He was born.
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