Music is such a big field. Every teacher is different. Every student is different. It's pretty much a matter of finding a match that works. I guess you should just try a teacher out.
Piano lessons are really adventures in psychology.
If the student becomes engaged, then everything is wonderful. Being engaged and on-task is what learning is all about. If things don't work out too well, then find a different teacher. Sometimes a good match just can't be found. But don't feel bad.