Jehovah's Witnesses make many, many sacrifices in their efforts to obtain paradise, and in the process thereof can see themselves as special, as superior to non-Witnesses, as belonging to 'the greatest organization in the universe.'
Apostates call this into question and can bring this entire house of cards tumbling down given their knowledge of the movement's history and foibles. Beyond the Governing Body's warnings to avoid such sites, which leads Jehovah's Witnesses to fear detection and discipline, there is also, I suspect, a natural fear of having their faith undermined and called into question, which inevitably affects Jehovah's Witnesses confidence and self-respect, if not pride. Apostasy is not just an intellectual issue for Jehovah's Witnesses: it's deeply personal.