I’ll try and write more as I settle in somewhere for the night (I’m in an airport at the moment), but Christmas is not celebrated on December 25th everywhere - this is the date for the Solemnity in the Christian West (where Latin Christianity prevailed and developed, being fractured by the various Protestant and Reformed movements), but not in the East, where Christmas is celebrated in January (January 7 in 2020 for most Eastern Orthodox, though others have different dates) or even June. The date for Christmas (in fact the Solemnity itself didn’t rank highly in the early Church, unusual as that seems now) wasn’t set in the first centuries following the death of Christ, and had origins in various ways of reckoning it (e.g. linking it to John the Baptist’s date of conception according to Scriptural markers).

Pope Emeritus Benedict XVI, who wrote a series of books (no surprise) on Jesus of Nazareth including The Infancy Narratives, puts forward that the date is assigned according to the date Christ died. Christ was believed to have been conceived and to have died on the same day - and, as His death was reckoned as March 25, dating this as His conception leads to a December date as for His birth.

Though it’s common in modern “pop religion history facts” to link the celebration to pagan festivals, these (like Mithras) either lack any authentic connection to the Christian celebration (i.e. Mithras and Christ being the same, with the former morphing to the latter under Constantine), were generally established later than when Christians began marking the Christmas holiday, and would have been avoided by Christians avoiding paganism and pagan rituals at the cost, not long prior, of death.