He is passionate about music. Notice how he knows the names and titles of songs. It's clear through three entire story.
Just because someone is passionate about something it doesn't mean that they possess what's necessary to study about it, nor that they want to :) moreover, Taeyi never really mentioned or hinted that he wants to study music, so I was surprised...
Those who can't do, teach. Who knows since he loves music so much he can find multiple ways to pursue a career
As a singer, teacher, or even a music manager. But you're right they never said what he wanted to do. But I don't think it's a stretch.
Am I the only one surprised Taeyi is going to music college? Like, what is he going to study there? Can he play an instrument? Is he that good in singing? (￣∇￣")