Writing is supposed to have therapeutic qualities.  Setting things down on paper is meant to help get them out of your system. I'm not sure how true that is.  Reading through what you've written afterwards might make you see how ridiculous you or your worries were, on the other hand it might keep old grievances alive.
For writers, there's always the benefit of being able to use your outpourings on paper in future work.  Writing about arguments can be particularly satisfying.  You can make your adversary obnoxious, give them a silly voice or a wart on the end of their nose.  You can also use all those witty comments and unanswerable points that you thought up when the moment had passed.  It's an opportunity to be as insulting as you like without losing your ladylike/gentlemanlike reputation–providing, of course, that you make sure no one recognises the person you're writing about.  After all, you wouldn't want to add being sued for libel to your troubles.