First, what is Christmas and why is it celebrated on December 25th? This is taken from Wikipedia:
Christmas is an annual festival commemorating the birth of Jesus Christ, observed most commonly on December 25 as a religious and cultural celebration among billions of people around the world. A feast central to the Christian liturgical year, it is preceded by the season of Advent or the Nativity Fast and initiates the season of Christmastide, which historically in the West lasts twelve days and culminates on Twelfth Night; in some traditions, Christmastide includes an Octave. Christmas Day is a public holiday in many of the world's nations, is celebrated religiously by a majority of Christians, as well as culturally by many non-Christians, and forms an integral part of the holiday season. In several countries, celebrating Christmas Eve has the main focus rather than Christmas Day.
Although the month and date of Jesus' birth are unknown, by the early-to-mid fourth century the Western Christian Church had placed Christmas on December 25,] a date that was later adopted in the East. Today, most Christians celebrate on December 25 in the Gregorian calendar, which has been adopted almost universally in the civil calendars used in countries throughout the world. However, some Eastern Christian Churches celebrate Christmas on December 25 of the older Julian calendar, which currently corresponds to January 7 in the Gregorian calendar, the day after the Western Christian Church celebrates the Epiphany. This is not a disagreement over the date of Christmas as such, but rather a preference of which calendar should be used to determine the day that is December 25.
Although it is not known why December 25 became a date of celebration, there are several factors that may have influenced the choice. December 25 was the date the Romans marked as the winter solstice, the shortest and darkest day of the year, and the first day in which the days would begin to elongate and the Sun would have a longer presence in the sky; Jesus was identified with the Sun based on an Old Testament verse. December 25 is exactly nine months following the Crucifixion of Jesus, which, around the 3rd century, became associated with his conception based on understandings at the time of the way salvation is bound up in birth and death; some theories then had the date of the Crucifixion as his birthday, others took the date nine months later: Christmas day. Also, Ancient Romans had a series of pagan festivals near the end of the year, and Christmas may have been scheduled at this time to appropriate, or compete with, one or more of these festivals. Some scholars disagree with this latter interpretation and state that the Roman Emperor Aurelian placed a pagan celebration on December 25 in order to compete with the growing rate of the Christian Church, which had already been celebrating Christmas on that date.
Now that you know the history of Christmas, is it okay to call it Xmas? Does calling it Xmas really take Christ out of Christmas? I mean, technically yes, but in reality no. There is a common misconception that the word Xmas stems from a secular attempt to remove the religious tradition from Christmas by taking the "Christ" out of "Christmas", but its use dates back to the 16th century.
Xmas is a common abbreviation of the word Christmas. It is sometimes pronounced /ˈɛksməs/, but Xmas, and variants such as Xtemass, originated as handwriting abbreviations for the typical pronunciation /ˈkrɪsməs/. The "X" comes from the Greek letter Chi, which is the first letter of the Greek word Χριστός, which in English is "Christ". The "-mas" part is from the Latin-derived Old English word for Mass.
So in the end, who cares if you call it Christmas or Xmas, you are still saying the same thing. I might just start saying Merry Xmas just to irritate Christians who do not know the full meaning behind it. But people who say Happy Holidays instead of Merry Christmas, well that is a discussion for another time, or never.
Just a more you know moment, the logo below is often called the Chi-Rho, is a Christian symbol representing Christ.