"Let's go around the room and share a fun fact about ourselves." This sentence produces a specific kind of anxiety in a significant portion of the people who hear it. Not because they are not interesting people. Because they are now required to produce evidence of their interestingness on demand, in public, in a professional context.
Why the fun fact is hard
The calibration problem. A fun fact must be interesting enough to be worth sharing but not so personal that it feels like oversharing. It must be surprising but not alarming. It must be memorable but not so memorable that it becomes the thing you are known for. This calibration is genuinely difficult under time pressure.
The competition problem. As each person shares their fun fact, the bar is set. If the first person reveals they have climbed a mountain, the person who was going to say they like cooking feels their fact is insufficiently fun. The fun fact becomes a performance.
The blank mind problem. When asked to produce a fun fact on the spot, many people's minds go blank. They know they have done interesting things. They cannot currently think of any of them. They say "I can't think of anything" or produce a fact that is not particularly fun. They feel embarrassed. The icebreaker has achieved the opposite of its goal.
What makes a good fun fact
A good fun fact is specific, brief, and slightly surprising. "I once spent three weeks on a research vessel in the North Atlantic" is a good fun fact. "I like hiking" is not a fun fact. It is a hobby.
The best fun facts are true, verifiable if asked about, and produce a natural follow-up question. They open a conversation rather than closing one.
How to have one ready
Prepare a fun fact in advance. Keep it in your back pocket. Update it occasionally. When the fun fact request arrives, you will be ready. This is not cheating. It is preparation.
The alternative: If you are running a meeting and want to use a fun fact icebreaker, send the question in advance. "Come prepared with one fun fact about yourself" removes the blank-mind problem and produces better facts.