Perhaps not the most common myths about Christmas, but these are the ones I regularly have to interact with online.
1. Christmas is a Christianisation of celebrations for Sol Invictus
Given that the first indisputable *dating* for Christmas to Dec 25th is the same document (the Chronicon of 354) that first attests to a birthday for Invictus, possibly Sol Invictus, it’s impossible to assert that Christmas is derivative of Sol Invictus’ birthday, any more certainly than the opposite.
2. Christmas involved a deliberate strategy of taking over Pagan holidays
Patristic authors never talk about such a strategy, pagan opponents never accuse such a strategy, and Christian theologians generally spend their time telling believers to stay well away from pagan holidays. The earliest argument for this view is not until the 17th and early 18th century, with proponents like Paul Ernst Jablonski and Jean Hardouin. The earliest suggestion of deliberate ‘takeover’ or ‘replacement’ of pagan holidays is Gregory the Great commissioning Augustine in the mission to the Angles. Apart from this there is a 12th century Syrian suggestion from Dionysius bar-Salibi that it was shifted from Jan 6th to Dec 25th to replace Sol Invictus, but I think we can consider the 12th century far enough removed that this may not reflect what actually happened in the 4th century.
3. Christmas is just a take-off of Mithras.
Justin Martyr is the first to make a connection between Mithras and Christianity, and he’s accusing Mithras followers of copying Christian elements. Given that the Mithras cult appears to be a mystery-type cult, involves only the broadest typological parallels to Christianity, and was restricted to initiated males, it’s unlikely that Christmas took off from Mithras. Add to that, it’s not even clear that Mithras should be identified with Sol Invictus either.
4. Christmas is Saturnalia
Given point 2 above, Christians had no known interest in rehabilitating Saturnalia. Saturnalia also ended *before* Christmas, so if they wanted to co-opt it they should have moved Christmas earlier.
Wishing you all a merry Christmas…