Obviously it should be. It celebrates the birth of Christ. Churches are packed Christmas Eve. All the best Christmas Carols sing of the baby Jesus. Religious Christrians use the day to celebrate their God and how He so loved the world He gave His only son. It is a religous Holiday.
The thing is, though, Christmas is so ingrained in the materialistic American culture that it does not seem you have to be a Christrian to 'celebrate' the holiday. I certainly know several people who never go to church but still have Christmas trees and give / receive Christmas gifts. I guess you do not necessarily need to go to church to be a Christrian, but in fact, I specifically know of at least one guy who says he does not believe in God. He still does all those Christmasy things. I also once got a Christmas gift from someone of the Jewish faith.
So, we have all heard or read the saying: 'put the Christ back in Christmas.' Obviously whoever says that would agree that Christmas as currently practiced (generally) is missing a necessary part it needs to be an actual religious holiday. Given the number of commercials and ads, you might even call it more of a holiday for retail and commercialism.
And maybe the vast number of non-Christians or semi-Christrians is not necessarily a bad thing. Whether or not everyone goes to church or consciencely honors Jesus's birth, it still is a season of giving. Charitable giving is up this time of year. More people volunteer at soup kichtens and so forth. Lots of people spend significant time with family over the holiday. So even if Christ is not in everyone's mind, his Spirit is still around.
But still, I think a lot, maybe even most people celebrate the Christmas holiday without celebrating, or even thinking about Christ. Maybe that is cynical.
I probably did not explain myself well, but in a nutshell that is why I say Christmas is not really a Christrian holiday.
Nonetheless, I am looking forward to it. I'll try to remember to thank God that I get to watch my kids open their gifts and spend time with family that I have not seen in almost a year.