Thanks for reaching out about this here in the Community.
It'd be great for you to read this support site article and follow the relevant steps listed in it to see if what you reported gets fixed and you can then remove songs from your own playlists.
Furthermore, if the steps in the above-suggested article don't do the trick it'd be good to perform a clean reinstall and start with a brand-new as well as the most up-to-date version of the Spotify app. Take a look at this Spotify answer to find out how the clean reinstall procedure works for your Mac.
Hope you'll find this info useful. Let us know if there's anything else we can help with!
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