Why does the Doctor celebrate Christmas?
Why not Hanukkah, or kwanza or some Gallifreyan holiday?
Canon answer if possible, not just: the BBC celebrates it, thats why.
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I don't think the Doctor celebrates Christmas exclusively, though granted, his appearances in film do seem centered around the Christmas holiday. The Doctor celebrates celebrations. His is a life of challenge and strife and with the TARDIS he does not have to deal with the dreariness of Mondays or Tuesdays, he can have every day belong to any particular festivity he wants.
The Doctor spends a lot of time at parties because they bring out the very best (and sometimes) the very worst in people. But both of those things are what the Doctor is interested in, not the holiday in and of itself. The Doctor's interests lie in people, no matter what their shape, form, religion or celebration. Think of how often we see the Doctor attending parties even when he doesn't have a gift. In "The End of the World", he offers "air from his lungs" as his gift for the celebration. No one bats an eye. You try that at Christmas...
We see the Doctor taking River Song to a variety of parties and festivals during their "dates" while she was in prison. I can see the Doctor at a bar or bat mitzvah, just as easily, and I suspect weddings are his favorite events, but other festive events are likely to be equally satisfying.
There have been Gallifreyan holidays he has celebrated in the written Doctor Who stories such as the Feast of Omega, celebrating one of the very first Time Lords. (PROSE: Happy Endings)
The Doctor himself does not celebrate Christmas. The focus on Christmas in post-Time-War Doctor's life is a result of several factors:
The biggest reason is that all of his primary companions have been British (English or Scottish; not sure what Jack Harkness counts as), and they celebrate Christmas. The Doctor often returns them home for Christmas as a favor to them. Note that he usually refuses to actually "celebrate" Christmas, although he is always invited to dinner, and instead prefers to run off somewhere else.
He is particularly fascinated with Earth, humans, and in particular Great Britain. This means he tends to find himself in the area of Great Britain even when he doesn't have a companion. Since Christmas is traditionally a time of celebration in Britain, it's understandable that The Doctor would enjoy showing up during that time.
For many years, The Doctor ended up saving London from imminent destruction on Christmas, to the point that it became a running joke among the residents. In both "The Runaway Bride" and "The Voyage of the Damned", the fact that this happened on Christmas was entirely coincidental, but it certainly created a connection between The Doctor and Christmas in London.