The way I heard it, January 6 was an early Christian holiday which celebrated three events: The Transfiguration, the Baptism of Christ and the Visit of the Wise Men. I think the idea was to celebrate Christ's divinity, and these three events emphasized His divinity.
Then, over time, the celebration of Christ's Birth was added to January 6, making it four events that were celebrated on that date. Previous to that, I don't think His Birth was celebrated.
Then at some point, (perhaps the fourth century?) the celebrations were split up and put on different dates. Transfiguration was moved to the summer. Christ's Birth was moved to December 25, by everyone but the Armenians. In the West, the celebration of the Wise Men's visit was kept on January 6, and in the East the celebration of Christ's Baptism was kept on January 6. (Did the West put the Baptism on another date? In the East, do we have a date for the Wise Men?)
Anyway, the Armenians are the only ones to keep the tradition of having more than one event celebrated on January 6.
This is just something I have heard. I don't have any citations for it, but it makes sense. Does anyone know of anything in writing about it?