It seems at least one of the songs you are trying to transfer did not come from the iTunes Store, but was instead downloaded from the Apple Music subscription service. You don't pay for individual songs on the Apple Music subscription service. You pay one fee every month and have access to the entire catalog.
Songs downloaded from the Apple Music subscription service cannot be transferred to other devices like iPod Shuffles, because there's no way to verify the subscription status.
Make sure all the songs you are trying to transfer were purchased from the iTunes Store before transferring them to the shuffle.
If you select the Song view in the Apple Music app, actually purchased tracks will have a date in the purchase date column.
If they came from the Apple music subscription or other sources, the purchase date column will be empty for those songs. The iCloud Status column may have other info for songs from the Apple Music subscription service too.