If everyone can teach themselves anything they need to know then what is the point of having qualifications to do anything in this world? Are you trying to tell me that if I study rocket science hard enough I will be able to build a rocket which flies to the moon?
The reality is that in this life time of ours we have VERY LITTLE TIME. It is impossible for us to become masters at everything we attempt. With ANYTHING in life you will find your abilty will increase the more you spend time with someone who is much better than you. I find the best pianists are those who are modest and always willing to learn from others, those that are quiet, keep to themselves, hold all their knowledge back and disregard other peoples advice never achieve their potential.
A good teacher is not there to teach a student just HOW to play the piano, but how to practice, how to prepare/organise your study, the teacher offers encouragement, pushes you onward (since you have someone who listens to you play and gives critique, sets you expectations/goals.) A good teacher can percieve a a students musical thought process physically in the hands and also in the mind, the teacher then tries to show the student showing how improvement in physical touch and mental thought improves progress.
I have students who do not need any help technically, they physically can do pretty much anything they are interested to play, as a teacher I find these students much harder to teach because what do you teach? What do you teach someone who can technique is spot on and top class musicality? You aim to increase their rate of reading music and memorising, teaching them how to force the issue of concsious memory (mentally memorising what you have to do on the piano) to muscular (forgetting about the mental thoughts and producing a string of notes via an automatic touch) to sound memorisation (forgetting about the physical and using sound to cue our hands). In my opinion you can never stop learning here and the more people you talk with about it the better you get. I personally get better at these thought processes not by my own personal study but by constantly going through memory processes with my students at all level of piano playing. It makes my mind feel amused when I highlight say 5 ways to memorise a very simply grade 1 piece for a beginner student, it is something I would never do myself but it stretches my own imagination, my own pattern recognition etc etc.
The thoughts of everyone who studies music IS NOT THE SAME. How one person sight reads notes which inspires movement to the hands which produces a memorisation (conscious, subconcious, sound, muscular) thoughts in the head is all different. Some people seriously cannot read music, or they can but they simply cannot make the connection from what they read to the physical action it has to produce, or the process is super slow and inefficient, or they cannot understand have to develop/retain memorised material. Some students need to learn these tools before they could ever think about studying music themselves.
Some people have challenges in their own physical make up which makes learning by yourself very hard or even impossible. I teach a student with Asperges and he has a lot of difficulty making decision for himself, even though he could do it he will never have the confidence to do it himself unless their is some validation or his fingering is condoned by a teacher. I also teach young children who have been diagnosed with ADD, can you imagine how impossible it would be for these chlidren to learn music themselves without someone guiding them through it?
In the end the teacher is there only to guide, like a soccer coach for a soccer team. The individual players of a soccer team know how to play they have aquired their skills without one another HOWEVER, they can be a team full of champions or they can be a champion team, there is a big difference. This is related closely to the study of music as well. We all have these individual tools required to play an instrument, we might know how to sight read, we might know how to play notes on a keyboard, but unless all of our tools are working together in harmony we simply are full of champion skills which are disconnected, just like a team of champions who do not nkow how to work together, they will be squashed by a champion team, those who know how to work together.