As a former teacher (still tutoring music & math) I always believed that commitment and obligation was required on both sides: the teacher to do their best to inspire, guide and find the right 'key' that will help the student understand; and the student to work hard to master the lesson du jour. But personalities are an important factor on both sides. So is teaching style...but equally imporetant is the student's learning style. Some teachers teach the same thing to everyone and leave it to the student to be smart enough to sort things out. There's a big assumption there. Others teach to the individual. Either way, it's not until the student really gets it and owns it that the lesson has truly been learned.
Over the years I've dropped a number of students who simply weren't doing what was needed, telling their parents I could no longer honestly take their money. Other teachers may not be so honest.
"When the student is ready, the teacher will appear" is so true...but so is the statement that the best students aren't so much taught as they are mostly guided.
As Rowuk and others constantly remind us, improvement on the horn isn't just a matter of practice time - it also requires that the mind and ears be open and that every practice minute be directed & focused. Teachers can only do so much, after all. But the student also has to be aware of what is working for them or not; to be blindly accepting of whatever a teacher tells you is surely to become your own barrier to progress.
Local 357 brings up a good issue. If progress is not being made then clearly one or more key factors is missing on one or both sides. There are so many variables between any teacher-student pair that it's impossible to say it's this or it's that. Each case is unique.