My catholic friend has said to me that, since the Orthodox celebrate the Leave Taking of Christmas on December 31, we actually don't have 12 days of Christmas, but 7 (which really messes up my singing of the 12 days of Christmas). Is he correct? If so, why do we continue not to fast until January 5th?
Your friend is kinda right - we do celebrate the leavetaking on Dec 31, probably
because of another feast of the life of Jesus (his circumcision) which falls on January 1st. However, the non-fasting period associated with Christmas continues (as you well pointed out) until Jan 4th, and the 5th is a strict fast day in preparation for the 6th. The only thing I can think of is this: that the celebration around Christmas is many-layered, just like the Paschal celebration (7 days of Pascha, the Sunday of Anti-Pascha, another 31 days of resurrectional hymns, another Pascha (the leavetaking).
I figure that we have the 7 days of Christmas (one feastday, 5 of the period, and 1 leavetaking) because of the Circumcision, but the entire period is colored by the Birth of the Lord, until the 6th. (In fact, I had heard that the Orthodox reckoning of the 12 days would be Dec 25th-Jan 4th + Jan 6th, skipping the 5th because its strict-fasting and including the Theophany since the two feasts are so closely tied together historically).
All conjecture, but its the best I've got.edited to fix bad coding