The two principal claims for Christmas having pagan origins pretend that the early Church chose December 25 in order to divert Catholics from Roman pagan festival days. The first claim pretends that it replaced the ancient Roman holiday of Saturnalia, a time of feasting and raucous merry-making held in December in honor of the pagan god Saturn.
Now, the Saturnalia festival always ended on December 23 at the latest. Why would the Catholic Church, to diverge the attention of her faithful from a pagan celebration, choose a date two days after that party had already ended and whoever wanted had already overindulged? It makes no sense. No serious scholar believes this claim.
Horvat, M.T. (2014). Christmas Was Never a Pagan Holiday. Tradition in Action. Available http://www.traditioninaction.org/religious/e031rp_PaganOrigins.html.Last accessed 30th Nov 2015.