I totally agree with dongsang153. A piano teacher is very similar to an athletic coach – especially at the higher levels. As such s/he fulfils a diversity of roles throughout the musical education of the student:
1. The teacher actually teaches stuff. Things that the student is ignorant about, like notation, or chord names. The student could acquire most of this knowledge without a teacher, but the teacher can save a lot of time. This is what we usually most value a teacher for, and yet it is the least important of his/her attributions.
2. The teacher guides the physicality of the student’s playing: which movements are most efficient. In the beginning a teacher is very important in this area. However as the student starts to tackle the more difficult repertory, he must start moving away from the teacher and developing his own physicality, his own way of moving, which ultimately is very personal and cannot be taught. Yet, a teacher can still provide
criteria and guidelines for the student to apply when trying to decide which fingering and which movement is the most appropriate. Paradoxically it may be in this most personal of areas that the teacher is the most important in preventing bad habits from forming.
3. A teacher – again, especially in the beginning stages – can provide discipline, inspiration, motivation and interest (although these last two must ultimately come from within).
4. The teacher acts as a knowledgeable critic, pointing out to the students the areas where improvement is necessary.
5. Most of all, the teacher (should) teaches
how to learn which is the true prerogative for independence.
So when are you ready to be without a teacher? Simple. When you have learned how to learn. At this point the whole universe will become your teacher. Every single event in your life will be a “teacher” teaching you something. And you will realise that this has been going on all along, you simply did not notice. (Some people go through life without ever noticing it). In this sense you will never be without a “teacher”, or without learning something new everyday.
And if you ever become a teacher, you will realise that you never learn so much as when you are teaching.

Best wishes,
Bernhard.