There’s a wonderful expression floating around -- origin unknown -- that goes something like this: A teacher can fix everything except a lack of practice.
This is a two parter.
First, there is the importance of practice. There is no substitute. In fact, practice will often get you through when everything else is going against you. At my very first "professional" gig, (i.e. not a teenage garage band), I was very uncomfortable. I knew none of the people and none of the music. I’d never played my set in a hall like that before, and it felt totally alien. And yet I not only made it through, I got high praise from the band leader. Why? I'd had good training and I’d practised a lot.
Part two is about one of a teacher's most important functions: to correct. It's not that students are habitually screwing up and getting it wrong. Learning is about working your way toward a goal, usually in manageable steps. It's easy to forget, confuse, misconstrue, or get distracted. What seemed so obvious during the lesson may mystify once you get back to your practice room. So you do the best you can, knowing that your teacher will patiently guide you in the right direction at your next meeting.
The classic way of teaching -- and the superior way -- is one-on-one with a skilled coach. Classrooms are OK for theory, but for the intense physical and mental study needed to master a musical instrument, there is no substitute for a hands-on approach. It might be tempting to pick up a video-based course that contains all the material you need to learn your craft, and if there are no teachers in your area this might be a worthwhile option … or the only option. But who is going to clear up misinterpretations and keep you from forming poor habits? Who is going to help you define your goals and set a course on how to get there? And who is going to give you that much-needed feedback on your progress?
Teachers do far more than correct. They encourage; they inspire; they challenge. They are reservoirs of music knowledge and history. They are a hub of potential networking. Above all, they are teachers, and no matter how expensive the lessons may be, a good teacher is always an incredible bargain.