Sounds convincing. But I found a flaw. Typically birds take their winter holidays in the warm continents, they don't shelter in caves. So birds would have gone extinct also. But they didn't.
So maybe they did shelter in caves, such as bats do, and then later decided it would be more appropriate to spend their winter holidays at the French Riviera or Cancun and not in their caves anymore. Because the bats messed up all those places. A stretch