I'm a long time Spotify user. I started using it long before the library feature was introduced, so my music collection grew as one big playlist. When I started with Apple Music, I wanted to use the library instead. I started to move my collection from Spotify to Apple Music by adding tracks to my Apple Music library.
After moving about three hundred tracks across, I opened Apple Music on my iPhone and looked for the option to download my library. I could not find it, and after some searching assume that it does not exist. It seems that in Apple Music only albums, tracks, and playlists can be made available offline (I'm not sure if this is the same case with Spotify).
This limitation is actually very easily circumvented with smart playlists. A smart playlist with one rule—Media Kind is Music—does the trick. It'll automatically include any music in your library, so when it's set to be available offline, all of your library music will be too.
It did occur to me, though, that the library may not be offlineble for a good reason. Whereas I'd add single tracks (often culminating in entire albums) to my Spotify playlist, it'd be nice to add various albums I'm interested in to my Apple Music library without having them sync offline. There is another filter that you can add to a smart playlist—Loved is true—that when used in combination with the media kind filter will include only music that you've loved. Maybe that's a better setup than simply offlining all library music.
Hopefully this is handy for somebody trying to do the same thing. If you know a better way, Tweet me!