Are you kidding me? Christmas is 100% stolen from pagan traditions. The tree and giving of gifts are flat-out stolen from the Roman holiday Saturnalia. The timing of "Christmas" was to absorb the pagan celebration of Winter Solstice. The entirety of what Christians think to be their special day is stolen and patched together from the other religions that Christianity steamrolled over. Rather than stamp out the traditions, they just included them in their own faith, because it's a lot, lot easier to get people to celebrate your version of their holiday than it is to tell them they're not allowed to celebrate it at all.
The only thing circumstantial is Jesus having been born in December at all.
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