This connects with the weight training example, where pushing yourself beyond where you think you can push yourself is vital. Perhaps that is the sole purpose of any effective “teacher”, be it sports coach, school teacher, or PhD supervisor — to kick, cajole, convince us that what we think is a limit, is not.
And it may mean that the old advice given to kids of “it doesn’t matter how you do, as long as you do your best” is misguided. Because how do we know we are doing our best if not by having someone else show us (possibly a competing student) what is possible?
Sgt. Carter could only kick you into being an expert rifleman, not an expert violinist. And Josef Gingold wouldn’t have been much help with your kalaripayat. Expert teachers can teach you new strategies, notice a subtle, but critical, bad habit, or remind you of what hasn’t yet become a good habit.
Regarding “it doesn’t matter how you do, as long as you do your best”, I think that is just a reminder to set internal goals rather than external goals, such as winning. Even as a strategy for winning, that’s sound advice. Don’t keep your eyes on the prize, keep your eyes on the price, and make sure you pay it.