O am learning piano. Someone I know is also learning but they say that a good teacher will stretch you and give you pieces that are beyond your capabilities. I dont believe this. My teacher only gives me things to play that are at my level. If they are too difficult I will not be able to play them.

Teaching is so fun ! and questions from students can be even more fun.

I teach different students differently. It depends on what their goal is, who they are playing for, and their own personality. I have 3 private students who happen to be in the same high school section. As recently as last week I was asked, "Why do you do Mozart with Jeff but not with me?" , Why does Amanda get to use one of your mouthpieces but I am still using this one?".

Some students cannot take constant assignments are too hard and un-completeable. If your teacher fits your personality and you feel you are learning then that is a good match. To be sure you could ask your teacher for harder assignments for awhile, or take a couple lessons from another teacher for a month and see if you like that method better.

Each of my private lessons is personalized and I try to find something in the lesson that also applies to their personal life and hobbies they are interested or involved in at the same time. They need to progress, yes. And sometimes I do give them something way out side of their capabilities ( and they usually do much better than they think they will).

You do need to be pushed at some times, most importantly you need to be learning how to learn and how to practice without your teacher. When was the last time you actually had a lesson with your teacher where you actually practiced during the whole lesson? It is invaluable to know how to practice correctly.

It depends...
http://youtube.com/watch?v=-vB59PkB0eQ
[Watch that, it wasn't originally for this analogy, but it works]
You have no idea how far you can go until you try.
Maybe that's what the teacher is doing.