Let B be some belief you don’t agree with, and A some popular argument for B. You believe B is false, but publicly criticising B is socially costly.
One strategy is to firstly assert B, but say it’s a shame people argue for B on the basis of A. There are many strong arguments for B, you say, but A is unsound. A has false premises, or invalid logic. So we shouldn’t use A to support B – otherwise the evil critics of B could use the unsoundness of A to cast doubt on B! True believers in B can safely disregard A, because we know B is true.
By using this strategy, you might plausibly persuade people that A is false. And because A is a commonly quoted argument for B, you have therefore made some progress towards getting people to reject B, all while avoiding the social stigma associated with B-deniers.