Hello tru6794,
Thanks for your post. I see that you’re being asked to join Apple Music to listen to music that you already own. I know you would like to listen to the music without repurchasing it. I’ll be more than happy to help.
If you had Apple Music for a while, some of the songs on your phone that were matched from either purchases or items you might have imported from a CD probably have the Apple Music version with a DRM that requires a membership. To fix this, you can delete the songs from your iPhone, and re-download past purchases. To put back the songs imported from CDs, you’d need to sync with iTunes on your computer. Take a look at these resources:
Sync your iPhone, iPad, or iPod touch with iTunes on your computer using USB - Apple Support
Download your past purchases - Apple Support
Take care!