My purchased CD's won't play unless I'm logged into Apple music! WHY???

Recently I went away to a cabin in the woods with no wifi or internet in the area. I couldn't play songs I'd copied, from purchased CDs onto my laptop and then copied onto my iPhone. I hate the fact that if I don't have internet I can't play my music! Surely there must be a way to play music without being on the internet? I kind of understand if I'd purchased the music as a download off the web (though even then, if I bought it, why can I only access it online?!) but there's no logical reason for my CD's to be turned into 'online' music! Is there a way to play my music when offline or do I have to find a less controlling app?? >:-(((