One simply cannot cross Christ out of Christmas, because the cross itself is Jesus' name. Advent during the holiday season reminds us that we are in, but not of, the world. Liturgically, Advent is a penitential season like Lent. Everyone seems to understand Lent. No, we take Lent very seriously as a time of fasting and meditating on the cross.
Advent is a similar season of preparation.
Traditionally, it was a time of prayer and fasting in preparation for the coming or advent of our Lord. The first Sunday in Advent focuses on the Second Coming of our Lord. Gradually, the focus shifts to waiting for Jesus' birth. Now the celebration begins. So it is with Christmas.