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.
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: