Where does christmas come from? Is it a christian holiday?

Today in my school I got into an argument with a group of christian friends over the fact that christmas is not a christian holiday. I believe that it is not, because i believe that it carries a nonreligious belief of family and friends and most christmas traditions come from the pagans and other religions. Only the name is provided by the christians. They argue, and i use that strongly, that it is a christian holiday because it celebrates the birth of baby christ and the NAME has christ in it. It is celebrated around the world by many people not for a single religion. I have no religious affiliation and i only go based on the historical facts.