Unfortunately, you aren't agreeing to disagree with just me but with Musicology itself: songs are a form of musical composition, with lyrics, for voice(s) and a subset of Music, differentiable from Music per se (which is the organisation of sounds into a, usually melodic, structure and may, but need not, include the human voice as one of its elements).

There are composers/artists/acts (such as the Cocteau Twins) who have experimented with songs using the human voice to sing in non-language, just as there are those (like Einstürzende Neubauten, for instance) that have experimented with making music using the environment rather than instruments. But that does not mean that the grey area between the two means that there is no difference between them at all, any more than does the existence of the duck-billed platypus mean there is no difference between mammals and reptiles or the fact that male seahorses gestate their young mean there is no difference between male and female.

I'm not arguing that songs aren't musical but that they aren't Music.