The Hairy Arm
Like everything else, it's all about attention.
The Origin Story
I feel like it's taken me an awful long time to tackle this one. And honestly, I've always used the term for a slightly different situation. This particular origin story starts at Disney animation in the 30s or 40s, and apparently the term "hairy arm" is quite literal. I've also heard this graphic design origin story. Again, literal hairy arm. And while not the origin of the term, there's this story (SFW) of the extra 4-minute marionette sex scene used as a Hairy Arm at the beginning of Team America: World Police to distract the censors. The story you know might depend on the industry you're in, but the gist is always the same. This from the Disney story:
FREASE: Right. They would add extra - well, they would add hair. They didn't want hair at all apparently. And then, they would bring it into the big meeting with all the head honchos. And those guys would say oh, well, you've got to get rid of the hair on the arms. And they would kind of be distracted from all the other things they had added to the character. So that's where the term comes from. It's basically something you add to a design that you know you may not even want there, but it's a distraction from your client or creative director. –Source
So, the Hairy Arm in its original form is an intentional misdirect of attention. It's a sleight of hand. If there is someone who always needs to have input or feel they participated or needs to say no to something, this version of the Hairy Arm allows you to acknowledge that desire in a way that is controlled.
The Unpredictable
What I always thought the Hairy Arm to be is something completely unknowable and unpredictable. Although it has the same effect on attention. You present the creative or you're on set, and the reviewer becomes laser focused on some particular aspect of the design. Maybe that's not quite the right shade of orange. Or they go back and forth on the usage of one word. Or they're not sure if the image is just right. It's not a "this thing is all wrong" kind of situation. It's very specific. One time someone became ultra fixated on the talent's eyebrows. Could not stop talking about it. Who would've predicted that?
You can never predict with certainty what someone will actually focus on. No matter how well you think you know a client, you can't really know what's in her mind or predict what her reaction will be to every detail. Second-guessing can burn up a lot of energy without giving you any more control. –Source
And that's my experience – you have no control over what will be a Hairy Arm. We all have little things that drive us nuts from time to time. Sometimes people just cannot tolerate one more thing not going their way in a day. Or, they decide to give actual voice to the little voice in their head. There can also be decision fatigue. Or, like the article says, they just want to feel useful.
The Actually Useful
But while my version of the Hairy Arm is unintentional, it has often worked to my advantage in the exact same way for the exact same reasons. It is typically a small, very specific element. And when someone's attention is wholly focused on this one small element, that means they are NOT focused on any of the other elements.
Often, that one small element is worth sacrificing for the greater good. Talk about the eyebrows went on all day on set. In this case, there wasn't really a solution – you can't just pluck their eyebrows. But there was not much issue with absolutely anything else that day. Half of graphic design is directing attention. The Hairy Arm (or Eyebrow) is not really so different.