A good musician is not necessarily a good teacher! Even a great teacher is not the right fit for each student. Sadly, a large number of teachers will not refer a student elsewhere either because they don't know they're not a good fit, or they just want the money to keep coming in. Far too often, teachers see their students more as customers than as musicians. Here's what good teachers usually look like:
Teachers should care more about the student than the music. There is no particular curriculum that is inherently better than the rest. A teacher who swears by just one set of books is more likely to teach the music instead of teaching the student. Some songs are just boring for certain students, and that should be a good enough reason to try a different song. Beware of teachers who constantly push every student to become proficient at every song in a particular book. There should always be a better reason to work on a song than, "It's the next one in the book."
For aspiring professional musicians, repertoire eventually becomes an issue, and a teacher should guide a student through the pieces that are critical to the student's success. Even then, the teacher should be looking primarily toward the student's success.
A good teacher is a musical mentor, not just a giver of assignments. All the best, most influential teachers make themselves icons or role models, in some way. In some cases, that role is inherent. For example, the teacher has achieved some major goal or gained some celebrity. However, most every teacher, regardless of popular stature, must find a way to make their lives personally attractive to the student. This is usually done through relationship. Good teachers should take an interest in the person in front of them, not just the music on the stand. Remember, the perceived value of instruction is always filtered through the perceived legitimacy of the person giving it. If you don't respect your instructor, you will likely devalue the advice you get from them.
He or she will ask if the student understands and have the student play part of any new assignment before it goes home with the student. Students get better between lessons, not at them. A good teacher will be sure that the time spent at home is going to be effective and efficient. Therefore, a good teacher must be sure the concepts presented are fully understood before sending the student home to practice.
At the end of the day it boils down to one thing: If the student seems excited to play the instrument, but consistently leaves the lesson less excited than they arrived, it’s time to find a new teacher!