The art of teaching is something which grows in one, not simply by doing a lot of it, but by putting together the necessary tools, learning from great teachers, and finding your own personal style. Like anything else in music, if you just copy others, it is a failure. A picture of a beautiful tree may look nice but it can't bear fruit. A teacher must become a great tree, with roots, with experience (the trunk or process of the tree) and ultimately fruit of its own. (See A Note To Students for more on this.)
A few things often go wrong in the teaching session. Even very good intentioned teachers sometimes make these errors. The first is to simply give students what the teacher studied, what worked for them. While classic technique and repertoire is certainly necessary, if the teacher knows in advance what the student's program will be, the teacher is not working in the moment or with the real humanity of the student. This can crush even high potential students and is not creative. Each student has their own time to blossom, and that should always be respected. For the teacher the art is to find the perfect key for the precise moment at each stage of a student's development, without putting a judgment on what stage that may be.
Only somewhat better is the teacher who gives to a student something which has helped another student in the past. "I had really good results teaching this to so and so a year ago, so here it is for you." The difficult thing is to know what is the best thing for a student in exactly the place where they are. Many people have good things to teach, but teach them in the wrong order for a particular student, or in no sense of order at all.
A teacher should have a systematic understanding of as many aspects of the instrument as possible, and, of course, how playing techniques work with harmony and all the other aspects of music. From this systematic understanding each student can truly be approached individually and solutions for unique problems can be found and built upon in a sequence which allows each student to sound like a perfect version of themselves (not a version of the teacher). From a systematic knowledge a teacher can draw solutions like water from a well which never runs dry; since it's a well of understanding and not just water, each bucket is especially designed for the student personally, and is not the same for all the thirsty people. Each solution of a problem provides the classic teaching of an important fundamental method, and in this way each student gradually develops the complete picture, arranged in a unique way for them. Students then have the tools to become their own masters, holding a complete understanding of their instruments and music. The traditions of performance are now being passed on without the dilution which is so pervasive in today's culture.