You may have found information that convinces you Watchtower is not the truth, yet when you discuss it with family or friends, they dismiss it as unimportant. They may even become angry and attack you and your motives. The reason behind this reaction is referred to as cognitive dissonance, which describes why people retain a belief despite being aware of evidence it is wrong.
When two musical instruments are played out of tune the grating noise is called dissonance. When a person is confronted with conflicting pieces of information, the inconsistency similarly creates discomfort.
When presented with reliable information that conflicts with an existing belief, it is not difficult to accept if it does not harm the person in some way. However, if accepting the new information will result in harm, a person will actively seek ways to dismiss the information. They will either ignore the information, justify it as unimportant, or dismiss it as false.
This phenomenon was studied by Leon Festinger. Festinger coined the term cognitive dissonance after researching members of Mrs. Marian Keech’s alien cult. Keech claimed aliens from the planet Clarion told her they would destroy the world by flood on December 21st 1954, with Keech and her eleven followers as lone survivors into a new world. The failure of this prediction did not stop the followers believing in these alien messages; all but two members became more active promoters of their belief after the prophecies went unfulfilled. Rather than accept being wrong, they instead justified the inconsistency by claiming world destructive had been prevented because of them.
Festinger identified ways people attempt to eliminate the discomfort of dissonance.
“The person may try to change one or more of the beliefs, opinions, or behaviors involved in the dissonance; to acquire new information or beliefs that will increase the existing consonance and thus cause the total dissonance to be reduced; or to forget or reduce the importance of those cognitions that are in a dissonant relationship.” (p.25)
When your family question the validity of information you show them, or attack your motives, it is their way “to forget or reduce the importance” of the information, in order to avoid the cognitive dissonance you are creating. To accept Watchtower is not the truth would mean your family lose their current hope for the future, their current group of friends, and have to accept they have wasted a large part of their life.
It is important to understand this common and powerful human tendency will make it difficult for you to convince others to accept what you believe over their current belief system. If discussions with your family have been volatile and unproductive, it is better to step back and rethink whether you should continue such discussions with them. Often a better long term strategy is to avoid attempting to change what they think, and plan to fade away from the religion in a manner that will allow some level of contact in the future.
 Leon Festinger, Henry W. Riecken, and Stanley Schachter, When Prophecy Fails, (New York: Harper and Row, 1956)