With experience, a teacher will be much more able to assess at what pace you or your child should be learning.
As a piano teacher, I'm always looking for new materials and pieces to teach. Over the years, I've amassed a large repertoire of piano music to teach from, which should suit most tastes and all abilities.
By having studied how to teach the piano, and not just how to play the piano, a qualified piano teacher is more able to get the best from, and to adapt to, his pupil. Personalised lessons are planned with each individual in mind.