This last is doubtful. There were serveral dates for the Birth, all calculated by varied means. None of the calculations had anything to do with copting anything, there is no reason to suspect the dudes who did the calculations of anything like this. Now, then, of those various dates, the reasons why the Church picked Dec 25th are unknown, and it is possible that “co-opting” a Pagan holiday might well have entered into them.
But then why Dec 25th? The Solstice was a few days earlier (depends on what year we are talking about the calendar was mutable back then). The big holiday around that time was Saturnalia, which was Dec 17-24, not on the 25th at all. It could have been to co-opt Dies Natalis Solis Invicti, but that was only celebrated by the Mystery Sect of Mithraism,which only become popular about the time Christianity did. Besides the Imperial Roman calendar was littered with holidays- just about any day picked would have come within a week of some holiday.
I suppose it is possible, the Church fathers could have looked at the 3-4 possible dates given by the “experts” and picked the one that had the biggest chance of co-opting a Pagan holiday. But if so, then why didn’t they push Christmas? Christmas didn’t become the Big Holiday until sometime in the Middle ages, by which time any possible competition with Saturnalia or Dies Natalis Solis Invicti had been completely forgotten by almost everyone.
wiki "*The identification of the birthdate of Jesus did not at first inspire feasting or celebration. Tertullian does not mention it as a major feast day in the Church of Roman Africa. In 245, the theologian Origen denounced the idea of celebrating Jesus’ birthday “as if he were a king pharaoh.” He contended that only sinners, not saints, celebrated their birthdays.[citation needed]
The earliest reference to the celebration of Christmas is in the Calendar of Filocalus, an illuminated manuscript compiled in Rome in 354.[2][24] In the east, meanwhile, Christians celebrated the birth of Jesus as part of Epiphany (January 6), although this festival focused on the baptism of Jesus.[25]
Christmas was promoted in the east as part of the revival of Catholicism following the death of the pro-Arian Emperor Valens at the Battle of Adrianople in 378. The feast was introduced to Constantinople in 379, to Antioch in about 380, and to Alexandria in about 430. Christmas was especially controversial in 4th century Constantinople, being the “fortress of Arianism,” as Edward Gibbon described it. The feast disappeared after Gregory of Nazianzus resigned as bishop in 381, although it was reintroduced by John Chrysostom in about 400.[2]In the Early Middle Ages, Christmas Day was overshadowed by Epiphany, which in the west focused on the visit of the magi. But the Medieval calendar was dominated by Christmas-related holidays. The forty days before Christmas became the “forty days of St. Martin” (which began on November 11, the feast of St. Martin of Tours), now known as Advent.[26] In Italy, former Saturnalian traditions were attached to Advent.[26] Around the 12th century, these traditions transferred again to the Twelve Days of Christmas (December 26 - January 6).[26] The evening of January 5 was called Twelfth Night, a festival later celebrated in the play of that name by William Shakespeare. The fortieth day after Christmas was Candlemas.
The prominence of Christmas Day increased gradually after Charlemagne was crowned on Christmas Day in 800. King William I of England was crowned on Christmas Day 1066. Christmas during the Middle Ages remained a public festival, incorporating ivy, holly, and other evergreens, as well as gift-giving.[27] Christmas gift-giving during the Middle Ages was practiced more often between people with legal relationships (i.e. tenant and landlord) than between close friends and relatives.[27]
By the High Middle Ages, the holiday had become so prominent that chroniclers routinely noted where various magnates celebrated Christmas."
*
Cecil has said this http://www.straightdope.com/classics/a1_034b.html
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*History records no observation of Christmas before 354, and by that time there was no one around who remembered exactly when Jesus was born. Today, historians have all but given up trying to figure it out. They give his birth date as 6-8 BC (good trick, but this was no ordinary dude) and leave it at that.
Nobody knows exactly why Christ’s birthday is celebrated on December 25. One theory holds that this is the right date, postulating that Zachary was high priest and that the Day of Atonement fell on September 24, ergo, John the Baptist was born on June 24 and Christ dropped in exactly six months later on December 25. Modern scholars use this theory to get laughs at cocktail parties.
Another guess works backward from the supposed date of the crucifixion (March 25), figuring that Christ was conceived exactly 33 years before he died, True Believers having no use for fractional numbers. According to the most tenable hypothesis, Christ’s birthday was assigned to the winter solstice (December 25 in the Julian calendar, January 6 in the Egyptian) because the date had a ready-made pagan holiday, the “Birthday of the Invincible Sun” (or “ancient Saturnalia debauch,” as you put it)."*
So, although I admit your hypothesis is popular, there is no solid evidence for it.
