Remember when you took lessons as a kid and you never practiced? With the exception of a very select group of individuals, nearly everyone who has studied an instrument went through a time when they didn't practice. Even professional musicians like myself went (and go) through these periods. You went to your lesson with a guilty look, told your teacher you didn't practice, and then everyone sighed and your teacher managed to fill the next 30 minutes with guilt-ridden teaching. Or maybe you thought you could get away with it, and just fake you way through it. Teachers know.
Listen, it happens. Sometimes practicing takes a backseat to other important things. And your teacher wasn't really all that mad at you because you had let them down. Your teacher was mad because it sucks to teach kids who don't practice. That's the secret of music teachers. We might say, "you're really letting yourself down", which in some cases is true with particular high-potential students, but overall a 30-minute lesson (or god-forbid a 60-minute lesson) with an unprepared student is hell.
Also, little version of you, you're not the only kid who didn't practice over the last week. You're the first student of the day and I have 10 more students to go, only 2 of whom have practiced. That' one hour of interesting teaching and four hours of oh-my-god-when-does-this-end. And you probably feel exactly the same way.
I know, I'm getting paid regardless of whether the student practices. But a student who doesn't practice also doesn't improve, and a student who doesn't improve usually ends up dropping out of piano lessons. And a teacher who loses students feels: A) disappointed, B) frustrated, C) scared because of lost income.
For a teacher who has to struggle through an entire day of lagging students, it's easy to go home feeling like what you are doing has no purpose. It's easy to feel like you're just yelling at brick walls. Teachers in general are undervalued in our society and music teachers are as well. We have chosen a path teaching what we love (and in fact, music is something that most people love) in order to continue the tradition of musicianship. A music teacher is essentially serving a public good by contributing to a culture of music while sacrificing financial reward. To feel like your dedication to the public good isn't paying dividends is what feels bad.
Parents, students and future parents of students:
You (or your student) needs to practice. If they don't, your favorite teacher will burn out.