Why won't Apple Music burn to CDs?

Music from the Apple Music subscription service is DRM protected and requires an active subscription to play. If you could burn it to a CD, you'd either have unplayable tracks, or the subscription requirement could be easily bypassed and lead to rampant piracy.

You do not own Apple Music, you are only licensed to stream and play it on authorized devices.

Copying and burning to CDs is not allowed in that license.