Employee whispers all day long at his desk, having full-blown conversations with himself about things unrelated to work: 'He was arguing with himself over his personal life or people he knew.'

This is almost as bad as having a whistler in the office.

There's nothing worse than having a coworker who is annoying in a way that you can't quite call out without breaching professionalism. If you're a higher-up, you have more leeway to tell your employees that they shouldn't sing under their breath in the open-concept office. In fact, you probably should tell your new hire to knock it off if they keep singing Hamilton when everyone else is trying to focus on work. But if you and your annoying coworker are on the same level, you probably don't feel like you can tell them to do anything, let alone to stop. 

Is it more unprofessional to be annoying in a way that bothers your coworkers, or to tell your coworker that they're being so irritating that you can't get your work done? There's no single correct answer, so the annoying person often keeps being annoying until they leave the job or get fired, and the annoyed person has to grin and bear it until they quit or get fired. You can't communicate with your coworkers in the same direct way you do with your friends or family, because being too direct can come off as unprofessional.