Piano teacher

One of my students was having trouble with her writing today, and called me over. I figured out what she wanted to say, and told her what to write:

I want to be a piano teacher.

She dutifully wrote this down, but was not particularly happy with it. She and her friend stared at it and talked about how it seemed a bit funny. They wondered whether I had misunderstood what she said.

It seemed simple to me. What was the problem? I told them it was correct and moved away, but continued to listen to their chatting. It was a while before I finally figured out what the problem was.

She did not want to teach pianos. She did not even understand how that was possible. She wanted to teach PEOPLE.