Birdsong is Music

In chapter 8 of Why Birds Sing, Rothenberg shows the song of a mockingbird converted to sheet music. My question is how can composers and philosophers say that birdsong isn't music if it can be set to human music? The song of the mockingbird can be studied and reproduce. What more does the bird have to do for its songs to be considered music in the human culture. If a human can make birdsong, it should be considered actual music. I don't see how Hamilton can consider a bird's song unmusical if it meets all the requirements for music made by humans. Just because birds don't have culture, doesn't mean they can't make music. A lot of people in the world have certain cultures not accepted by others, but their music is still considered acceptable. So, why not birds?