You can always use the superior service, Spotify, as an alternative. :-D
Better music discovery. 320 Kbps higher quality tracks. More intuitive UI. Free add supported tier. Family subscription support.
Literally the only con of Sporify vs. Apple Music is that it doesn't have Siri integration, but that's only because Apple holds the key to that castle and they aren't letting anyone in.
I still am torn to be honest. I like the easy integration of AM on all my devices (I know Spotify has a Mac app but I play AM through Apple TV a lot). I like the visual appearance of AM and that there are lots of layers to explore. But there's a lot to be said about Spotify's simpler, more utilitarian app that is much faster and just works. I listen to AM with High Quality on Cellular toggled on....is that comparable to Spotify's quality?