Please note that many of the anti-Christmas polemics which affirm as a "fact" that Christians borrowed from Mithras or someone else come from well known anti-Christian writers like Christ-mythers. For e.g. Wiki says: "Originator of the
Christ myth theory,
Charles-François Dupuis, set out to prove the Mithraic origins of Christianity." More on that in a minute.
Here is a fascinating more recent study: "Revisiting the Fathers: An Examination of the Christmas Date in Several Early Patristic Writers Kurt M Simmons, JD: "
Editor's note: This article appeared in 98 Questions Liturgiques (2017) 143-180. The article documents occurrence of the Christmas date to sometime between the mid- first to mid- second centuries. Specifically, it demonstrates from heretofore lost or unrecognized excerpts of Julius Africanus (AD 160-240) and a work attributed to Evodius (died circa AD 64-68) that the Christmas date was an integral part of the Protoevangelium of James before it settled into its present form sometime in the latter half of the second century. The article then shows that the above conclusions are supported by a published article by Yale PhD candidate, Thomas C. Schmidt, which shows that Hippolytus (AD 170-236), a younger contemporary of Africanus, also almost certainly subscribed to the December 25th birth of Christ. The article concludes that the Christmas date therefore cannot be accounted for by other leading theories, and instead appears to stem from an early tradition (legend or report) whence it was received in good faith by the fathers of following ages." Taken from:
https://www.dec25th.info/Revisiting the Fathers.html
So, a recap:
(1) 2nd century writers - long before the 4th Century. - like Julius Africanus and perhaps even a work attributed to St. Evodius (
https://en.wikipedia.org/wiki/Evodius), a first century Bishop said to be one of the 72 disciples of Christ, state Dec. 25th as a Christian celebration of Christmas. The Protoevangelium of James mentions Zechariah as a High Priest ministering in the Temple on Yom Kippur when John the Baptist was conceived. Yom Kippur is in late Sept., as mentioned earlier, which agrees with a late March Conception of Christ, and a late Dec. Birth.
(2) So what happened in the 4th century exactly, and what is the connection to Mithras? Firstly, you will find all sorts of unhistorical nonsense from anti-Christian atheists on this, for e.g. the claim that Mithras was supposedly born of a virgin. Rubbish! As per the mythology, he was born of a rock! That is refuted here: "Some non-scholarly writers say that the birth of Mithras was a virgin birth, like that of Jesus. No ancient source gives such a birth myth for Mithras. Rather Mithras is always described as born from solid rock.
11"
https://www.tertullian.org/rpearse/mithras/display.php?page=Mithras_and_Jesus The link mentions the atheist writers who claim this with references.
To Wikipedia's credit, it correctly mentions that about Mithras: "Mithras was born from a rock. David Ulansey speculates that this was a belief derived from the
Perseus myths, which held he was born from a cavern.
[18]
And about Dec. 25th? Even that is far from clear. The original sources about Mithras don't mention any such thing. The same Wiki link continues: "Beck (1987)
[24] argues that this is unproven. He writes:
"The only evidence for it is the celebration of the birthday of
Invictus on that date in [the 4th century/354 A.D.]
Calendar of Philocalus.
Invictus is of course
Sol Invictus,
Aurelian's sun god. It does not follow that a different, earlier, and unofficial sun god,
Sol Invictus Mithras, was necessarily or even probably, born on that day too."
[24]: 299, n. 12
[d] "
https://en.wikipedia.org/wiki/Mithraism_in_comparison_with_other_belief_systems#25th_of_December
And so, the evidence that Christians borrowed anything, including the 25th of December date, from Mithras is very weak. The fact that Christians celebrated 25th December long before pagans did makes it far more likely that, if any borrowing took place, it was probably in the other direction, namely pagans taking it from Christians because of the rising popularity of Christianity. The link says: "Christian apologists, among them
Ronald Nash[16] and Edwin Yamauchi,
[17] have suggested a different interpretation of Mithraism's relationship to Christianity. Yamauchi, pointing out that some of the textual evidence for Mithraist doctrine was written after the New Testament was in circulation, makes a logical leap in considering that it is more likely that Mithraism borrowed from Christianity, rather than the other way around"
God Bless.