I may be totally off base here, but I think your T is just being cautious. I totally get how you are worried, but maybe he’s concerned that if you play a song and he doesn’t react in the way you are wanting that it will cause more harm then good.
For me, I appreciate music. Sometimes a song “speaks” to me, but more often then not, it’s background noise. Maybe your T is the same way? In a general sense, he may have been totally fine with playing a song in session. But take a client- you- who he knows feels and thinks about things deeply, and a song is no longer just a song. If it’s important enough for you to bring to session, it’s meaningful. And maybe he just doesn’t want to mess it up?
Oh, and for what it’s worth- my 7 year old daughter can’t figure out how to blow her nose, either. Drives me crazy, as my 5 year old daughter has figured it out, but it’s just one of those quirks that we deal with as parents!