For me, the idea and impulse of wanting to share music with someone to whom you feel a connection is a teenage desire. I am thinking of mixer tapes (or whatever these rebellious youngsters get up to these days with their Spotify playlists) sent to our hearts' desires in the hope that in hearing the music they will also hear our inner self. I think it is a lovely impulse and it reminds me of blossoming identities and passions. I would feel rejected in your position. It seems that your therapist is not welcoming your teenage self and that seems like a missed therapeutic opportunity.