Control Line Racing is typically flown with 2, 3 or 4 models in the same circle. Models are pitting at different times, taking off again and sometimes you may get your lines tangled with someone else's. Going without a safety thong allows the pilot to switch hands and unwind the lines.

Picture the thong hanging down from your wrist as you pass your hand over another (with a slower airplane) pilot's head. Maybe it hangs up with undesirable results.