Here’s what Henshall has to say about the etymology of 騒.
The left-hand side, 馬, is a horse, of course.
The whole right-hand side once meant “flea.” The top, 又, has evolved from a different shape that meant “hand.” And the bottom, 虫, is “insect.” A flea is an insect found on the hand or squashed with the hand, he says.
In 騒, the right-hand side acts phonetically to express “confusion” and to give the sense of “troublesome insect.”
So taken as a whole, 騒 gives us “confusion caused by insect troubling horse,” which has gained the broader and more general meaning of “noise” or “disturbance.”
All of this brings to mind an old song. I just checked the lyrics, and they’re even more appropriate than I remembered. An old woman swallows a horse to catch a fly that she swallowed at some earlier point. A faulty strategy, to be sure. But perhaps she had 騒 (with its horse-insect union) on the brain.
Ah … the plot thickens. At the end of the version to which I linked above, the woman thrives after eating the equivalent of a zoo. In another version, she dies. I guess you can choose your own ending.