How does data travel in a butterfly network?
The description you were given is indeed phrased in a confusing way.  I suspect they're talking about messages travelling from top to bottom.

I suspect by "output switch" they might mean "output from the processor" (input to the butterfly network), which is pretty confusing.  That explanation could have been phrased better.

Butterfly networks are described in many places.  You might want to find another description of butterfly networks and read that.