Airplay works only when initiated by Mac

My local music collection lives on my Mac. I should be able to use the Remote app on my iPhone to connect to iTunes and my local music on my Mac, and then stream music to Airplay devices using Airplay on my iPhone. And it seems as if I can: I'm able to choose an Airplay device -- the iPhone says it's working -- but the music isn't actually playing on my chosen Airplay device or on the iPhone, it's playing on my Mac. The only way for it to *not* play on my Mac is to go to the Mac and change Airplay device from there.

The good news is that streaming services work fine. I can stream YouTube, Pandora, Spotify on my iPhone, and use Airplay to output that streami wherever I like on the Airplay network. It works 99% of the time.

This must have something to do with how iTunes works.

Any ideas?

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