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Look at this another way. The artist makes money from their lyrics and can do so in various forms. That money amounts to (or adds towards) a living. They are the author and they own the copyright, unless they have sold the copyright to someone else, in which case you still have the same problem.
So what if it was you? If someone else took your work and made money from it, how would you feel? It's your work and wherever it makes money you are entitled to the sums involved. Further, you might not like the way it was used. Suppose a brilliant 'call to arms' speech in your story appeared in neo-Nazi propaganda widely distributed on social media?
For these reasons, copyright is assigned to the work, and that literally means they have the exclusive right to copy (or not copy) their work in as many ways and in as many forms as are possible and further, to have full control of when and how such copies are made. If someone buys the movie rights to your story, they are buying the copyright for the big-screen (or sometimes the small-screen) audio-visual medium, and that medium alone - and you no longer have those rights.
It might seem harmless to quote a couple of lines from a song, but you are impinging upon someone's inalienable rights to control of work they have produced, and arguably, making money from their hard work without recompense.