Mark Mulligan reminds us that Apple doesn't necessarily care if Apple Music makes money, there are afterall, easier ways:
In fact Apple could make a LOT more money if it simply decided to spend money marketing Spotify to iOS customers.
For argument’s sake let’s assume Spotify has somewhere in the region of 6 million US subscribers, that 60% of those are on iOS and that 60% of those iOS users pay via iTunes, Apple thus generates $8.4 million a month in subscription revenue from Spotify. To generate the same amount of US subscription margin from Apple Music, Apple would need 16.9 million US Apple Music subscribers (assuming an operating margin of 5%). In fact, in practice Apple will be in heavy negative margins with Apple Music due to its extensive marketing efforts.
Of course Apple isn't interested in Apple Music margins per se, since Apple Music, like the rest of the iOS ecosystem, is about adding value to entice new and existing customers to buy more Apple hardware. Still, it's fun to consider the possibility that Apple makes more money from Spotify than Spotify does.