An uncensorable, global, distributed data store opens up all kinds of possibilities for weaponizing data. If you're intending to blackmail* someone by threat of doxxing, threatening to put their information on the blockchain is much worse than simply putting it on pastebin.

People have also attempted to use blockchain data for coercion. For example some folks were worried about the centralization of Bitcoin mining in China, so they posted information about Tiananmen Square on the blockchain, hoping the Chinese government would simply ban Bitcoin.

*blockmailing them, if you will.