Why is Christmas called Christmas, if Christ isn't involved?

Question

Merry Christmas!

Answer 1

Originally Christ was very involved.
Christians wanted to celebrate God coming to earth to dwell among men. They wanted to celebrate His birth, but at the time no one really knew when Christ was born. (We now think it was in September around the year 4BC based on records from that era)
At some point, The Church arbitrarily picked a date near the Winter Solstice as that was a time when everyone else was celebrating Yule and Hanuka and a number of other events. It was simply a matter of convenience to set Christmas at that time.
Over the years, cultural traditions have blended and melded and bled over from the different celebrations. Father Christmas, Christmas Trees and Mistletoe are actually not involved in the Christian Faith, but were simply very popular traditions that were adopted by Christmas. Likewise, there are a number of Christian Christmas traditions that were adopted by others as well.
But at the root of Christmas there is still Christ. Santa, Eggnog and candy canes are certainly more common icons, but it isn't Santa that is on display in front of the local Christian Church. Christ is still there.

Answer 2

Because that's what the church decided it should be called, obviously. No "Christ" involved, of course.