Christians celebrate Christmas because it's the birth of Christ. Jehovah's Witnesses can't celebrate birthdays and thus they don't celebrate Christmas.
But there's more to it than that. Why can't Jehovah's Witnesses celebrate Christmas and other holidays if they want to? Why can't they celebrate birthdays? What's stopping them? Is it a personal choice? Or does their religion forbid it?
The simple and most truthful answer is that the Watchtower Society doesn't allow Jehovah's Witnesses to celebrate holidays. See the 2010 Secret Rule Book, Shepard the Flock of God. (only available to Elders).
Jehovah's Witnesses say that everything they teach is in the Bible. However the scriptures are silent about celebrating Christmas.
Regardless of what the Bible says or whether an individual's conscience would allow them to celebrate Christmas, celebrating holidays is forbidden by the organization. The only celebration that is allowed is the celebration of Christ's death. This annual event draws millions of Jehovah's Witnesses and is called the Memorial Celebtration. However even at this special event, Jehovah's Witnesses are not allowed to partake of the bread and wine unless they belong to 'the annointed class'
Those who do not obey, all the Society's rules are shunned by family and friends forever. Your family won't even go to your funeral decades from now if you are excommunicated or disfellowshipped. According to the Watchtower, it's 'God's command' not have even the slightest communication with 'apostates'. Watchtower magazine, April 15, 2012, Article: 'Betrayal—An Ominous Sign of the Times!', par 16, 17
All those who leave because they no longer want to follow Watchtower rules are treated as 'wrong doers'. Watchtower magazine, Sept 15, 1981, p 23, par 14-16. They are persecuted and hated by family members still trapped in the cult..
The practice of treating loved ones who leave their religion as if they're dead began in 1952. Since then millions have been shunned. Breaking up families affects Jehovah's Witnesses and non believers who have relatives inside the organization.
Because of the severe consequences of celebrating holidays such as Christmas, obedience is the best option for most Jehovah's Witnesses. Only the strongest and most authentic individuals are willing to give up their family, friends, and religion in return for their freedom.