We don’t have to like their personality to do a good job. At least not their whole personality.
But what does it need to be a good music teacher?
We should at least admire their interest in music. That’s what brought them to us. Also, it’s what we would love to see in them.
It’s what we have to focus on, especially if other character traits start to bother us.
The students’ wish to play music and our ability to focus on it are what makes us great teachers. Students benefit.
Additionally it’s what guides us through more difficult times of our job. When we have a bad time or don’t get along so well with parents or students, it is nice to remember: What brings your students to you is their love for music.
In that you are alike. So that part you should like about them, yes.