11 years ago, Lockhart’s Lament was published. I now offer an addendum to a point in Lockhart’s Lament.
The reason why people, even to those who love competition math, do not love math at school is for one very important reason: discovery. A great metaphor is the road less taken, and how staying on the path is not always the best option. Lockhart talks about how the education system teaches math in a way that is unappealing to students - this is because in competition math, the solutions found bring great pleasure to the students, whereas school math is extremely repetitive.
I think the best way to describe this is with examples. Very often in competition math, you are presented with a problem that, when done the right way, has a very elegant solution. However, school math sucks the joy out of it and instead replaces it with formulas in facts. This is analogous to how special cases often have beautiful properties (e.g. the equilateral triangle), but the general cases often exchange beauty for power. Math teaches power, when it really should be teaching beauty, at least in the earlier stages.
From what I hear about college, it seems that professors do a great job of combining power and beauty - but pre-college schools aren’t able to do this. I think this is not because they do not have the “funding” or “right materials”, but rather the desire to do so is not there. It is extremely hard to have a curiculum that teaches both the necessary skills applicable to jobs and have fun at the same time. And for this, I don’t think the school system should change - rather, it is important to spend your own time learning math, so that one can actually appreciate the math that is presented in your class in 5 minutes.
Note: This is not to point to any teachers - I enjoy my math classes despite not enjoying the curriculum itself. It says a lot about a teacher when they turn a very poorly designed lesson into something fun.