As a piano teacher, and as a mom, I dread hearing the words "I can't" come out of the mouth of a child. Since this is a music studio blog, I'll address this from the piano teacher's perspective, though.
When a beginning student hires me to teach them to play the piano, they are asking me to teach them something new. Something they are currently unable to do on their own. But something in their mind believes they can learn it, or else they wouldn't have even called me. Therefore, it is important that they continue to believe they can learn each required skill along the way throughout their lessons. Sometimes, it's my job to teach in such a way that nothing ever seems impossible. Other times, it's the student's job to just believe that "they can."
One of my favorite children's books is "The Little Engine That Could." You know the story. It was a tiny little engine who had to pull a big train over the hill. All the way up the big hill, the engine told himself, "I think I can! I think I can!" It's a cute little book with a huge life message in it for kids. So much in life is all about our attitude. This is very important in music. A student who gives up when they run into a difficult technical skill.....well, gives up. They're just done. However, the student who believes, "If I try hard enough, I can master this" will go very far.
So, how do I handle the "I can't" attitude in lessons? This kind of depends on the age and maturity of the student. Sometimes, I pull out their very first book and have them play the very first "song" they ever played (which is usually not even on the staff yet). Then we compare that to the most recent piece of music they mastered, and discuss how they came to be able to play that when they didn't even so much as know their finger numbers when they started lessons. Other times, it only takes this simple statement, "Yes, I agree. Right now, at this very moment, you can't [play that trill] very well. But we're going to work on it, and try different things. And, with time, it will get better and better." With young students, I sometimes have to get more creative, though. Here's an example of how I recently responded to "I can't" with a young beginner.
A young boy had looked ahead in his book, and was clearly distressed about the fact that the staff was most likely going to be introduced in this lesson. So much so, that he was actually disappointed that he passed all of his songs and was "getting" to move ahead in the book. Several times, he turned to a page with notes on the staff and told me, "I can't do that." Reasoning with him in any of my usual ways was, clearly, not going to have any impact on him. So, in a desperate attempt to overcome this, I pulled out a blank piece of paper, and asked him to write the words, "I can't" in big letters. Then, I asked him to carry the piece of paper out of my teaching studio and I escorted him to the receptionist's desk. We placed the piece of paper under a book so nobody could see it. Then, I told him, "Ok. Now the words 'I can't' are going to stay out here. You don't get to take them back into my studio. They are not allowed in your lessons." Of course, being quick on his feet, as he sometimes is, he says "What about 'I can not'? Can I say that?" I laughed and said, "No, sir. You may not." But he got the message. And we spent the rest of the lesson learning about the staff and the bass clef sign, and even played a short five-finger song.....reading from that staff. And he was proud of his accomplishment. As he left his lesson, I stopped him at the receptionist's desk and pulled out the piece of paper with those word, "I can't" on them. I had him tear up the piece of paper (his mom watching in amusement the whole time) and throw it in the trash. Then, I ended the lesson with, "There! Now you can't use those words at home, either. When something is difficult, you just try real hard until you get it right." He left with a big smile and his usual, "Thank you Mrs. Brown."
What did that boy learn in his lesson that day? Yes, he did learn that this thing called a staff has five lines and four spaces. And that the bass clef sign looks like half of a heart and it's job is to show us where F is. And he learned how to find his left hand C position notes of the bass staff. But I hope that, more than that, he learned that nothing is too difficult if you try hard enough. And new ideas really aren't that scary if you trust you're teacher to only give you what you can handle at once (we discussed this a bit after we got rid of "I can't").
I encourage you, as a teacher or a student, to replace the untrue statement of "I can't" with true statement, like, "This is really difficult", "This is going to take a lot of extra work", "I've never done this before", "I need some help figuring this out", etc. It's ok to acknowledge a challenge. But don't ever give up.