Jehovah's Witnesses believe that celebrating holidays is wrong. Why? Because they believe that most holidays fall into one of three categories. All three are wrong according to the Witnesses. These three categories are false religious holidays, political holidays, and holidays that honor anyone or any human organization other than God.
False religious holidays or holidays of pagan origin cannot be celebrated by the Jehovah's Witnesses because they believe that their God Jehovah requires Christians to belong to the 'correct' religion in order to be saved.
Belonging to a 'false' religion and participating in their false holidays is thought to be wrong. Examples of false religious holidays would be Christmas and Easter. All religions are thought to be false and dominated by Satan, except for their organization. According to the Watchtower, only Jehovah's Witnesses have any scriptural hope of being saved. Watchtower Sept 1989
Jehovah's Witnesses are politically neutral in world affairs. They are observers but do not participate. They do not vote, salute the flag, go to war to protect their homeland or do anything that would undermine their political neutrality.
Therefore Jehovah's Witnesses do not celebrate political holidays. They are separate from the world based on their interpretation of the Bible.
Political holidays would include independence day, memorial day, and veterans day.
Jehovah's Witnesses believe that if one honors a human institution, person, or animal, this is a form of 'creature worship'. They believe that God should get all the honor and glory. The Bible says, 'Salvation comes from the Lord.' Psalms 3:8
Celebrating holidays such as Mother's Day and Father's Day are considered wrong because it honors humans to excess.
Critics say it's odd that human institutions, people, and animals cannot be honored once per year. Why? Because their human institution, - i.e. the Watchtower organization is honored to excess 365 days per year as God's channel of communication to the world.
Jehovah's Witnesses are completely loyal to their religious leaders. Complete trust and obedience is expected. Questioning, independent thinking, and disagreement is not allowed.
If 'salvation comes from the Lord', why is the Watchtower organization given so much importance on a daily basis? Why does God need to be obeyed AND Watchtower officials?
Here's what the Watchtower says. 'By word or action, may we never challenge the channel of communication that Jehovah is using today. On the contrary, we should cherish our privilege to cooperate with the slave class. And should we not strive to be obedient and submissive to those taking the lead in our local congregation?' Watchtower Nov 15, 2009, 'Treasure Your Place In The Congregation', par 5. (Note: 'the slave class' and 'channel of communication' refers to the Governing Body of Jehovah's Witnesses. Based on Matthew 24:45-51)
* JW's are concerned about 'stumbling' people. e.g. JW's can't celebrate holidays, but they can have big parties or celebrations on any day, including Thanksgiving Day and Christmas Day. Even though they can, some of them will not. They may avoid having large celebrations on official holidays because they don't want to 'stumble' their neighbors and other JW's.
Because JW's can't celebrate holidays, they don't want people to think they're doing something that's not allowed. Instead, they may have a big family party the day before or the day after. In this way no one can say they celebrated Christmas Day or Thanksgiving Day.
Regarding 'stumbling' others, the Watchtower says this, 'Paul also said: “Keep from becoming causes for stumbling.” (1 Cor. 10:23, 32) In matters involving personal preferences, then, it is the course of wisdom to ask ourselves: ‘Am I willing to forgo certain rights when the peace of the congregation is threatened? Am I prepared to conform to Bible principles, even when it is inconvenient to do so?’ WT, Feb 15, 2009, Article: 'Should You Insist on Your Personal Preferences?' par 2
Stumbling someone or appearing to be hypocritical is also a consideration when accepting gifts on holidays or around the holiday season. Even though JW's can't accept or exchange Christmas presents, some JW's may in good conscience accept gifts around Christmas time if they're not wrapped in Christmas paper and if they're not obvious 'Christmas presents'. If you give them a gift on Christmas day and tell them it's NOT a Christmas present, some JW's might accept it. Others will not accept it unless it's the day before or the day after. Technically JW's CAN accept gifts any day of the year. However the gifts cannot be linked to any holiday they can't celebrate.
Although celebrating holidays is strictly forbidden, you might have a JW friend or neighbor who secretly celebrates holidays. Many claim to be Jehovah's Witnesses because they don't want to be shunned by their JW relatives. These JW's are not 'active'. They rarely go to meetings and perhaps never go door to door preaching. Millions of these JW's really don't want to belong but they've afraid of the consequences of leaving. They may not believe in some or all of what the Watchtower teaches. They might secretly celebrate holidays and accept holiday gifts if they believe they won't get caught and no one will report them to Watchtower Elders. 
1. Claiming to be a JW and celebrating holidays secretly seems hypocritical. The reason for celebrating holidays quietly is because the Watchtower's shunning policy is severe. Once your relatives start shunning you, it will continue for the rest of your life unless you 'repent' and go through a lengthy reinstatement process to prove you will be obey all Watchtower rules in the future. Shunning is FOREVER. Even 50 years from now they will walk right by you without making eye contact. They won't even go to your funeral. Here's a good article and video called the truth about Jehovah's Witnesses. Hundreds of JW's at a large convention publicly shun a man they think is 'disfellowshipped'. The theme of that convention was 'Imitate Jesus'.