Many teachers will tell you that they learn from their students. As a violin and viola teacher, I've found that teaching has helped me improve my practicing and develop my own musical skills. In fact, in some ways teaching has been more effective at improving skills like ear training than any of my classroom learning.
Listening and Aural Skills
A music teacher needs sharp ears. We have to identify when a student is out of tune or plays a wrong note and be able to immediately correct the problem. All this intensive listening has dramatically improved my aural skills. I remember getting so frustrated in my college classes; I didn't think music theory was my strong suit, especially the sight-singing! Now, I have plenty of practice singing notes on pitch, since I frequently encourage my own students to sing their pieces before they play them. Years of honing in on student's out of tune notes has also given me a better sense of melodic intervals and how particular notes fit into a chord. If my theory professors could see me now, they'd probably be shocked.
When I went to my first teacher-training class for Suzuki Violin, I did not expect that it would be one of the best classes in violin technique I'd ever had. Yet the more I teach, the less that surprises me. Teaching has made me think deeply about the fundamentals, since I'm constantly analyzing my students' technique, from their posture to how they hold their instrument or their bow. As I work with a student to solve their technical issues, I gain insight into the underlying logic of the violin and viola. All this focus and understanding has strengthened my performance abilities, from tone production to intonation to musical expression.
Looking back, I think I was too passive as a student. I was always waiting for my teachers to tell me how to play, instead of looking at the music and discovering it for myself. Now that I'm the teacher, I have to be the one looking of the music, interpreting it to the best of my understanding, and then finding a way to communicate that to a student. In one way, that's very exciting! I don't have to rely on anyone else when I'm practicing, and I can play the music how I see fit, not according to another person's ideas. What's more, my experience inspired me to teach my students how to analyze music on its own. The more I think that way about music, the easier it becomes.
Teaching and performing should not exist in separate spheres in a musician's mind. Instead, teaching can be an excellent opportunity for musicians to develop their fundamental techniques and listen carefully.