The greatest JW double think I can come up with is this -
The Watchtower advocates in its printed publications for all people to examine their religion for the purpose of finding out whether or not it is "the truth". Conversely, the Watchtower and its leaders, the Governing Body, prohibit their followers from examining the teachings of the Watchtower for their accuracy. To simply question a belief of the Watchtower is to risk being shunned by their organization. Followers are advised to simply accept what they are told and to question it is to question God. In short, that is the central belief of all Protestant/Reformation/Evangelic Christian denominations - Never question those taking the lead as that is the same as questioning God.
An unexamined life is not worth living - Socrates