It's not about solving that particular problem. They are teaching a method of problem solving. You're teaching a person to have different tools to solve problem

It's not about solving that particular problem. They are teaching a method of problem solving. You're teaching a person to have different tools to solve problems instead of just relying on the methods they already know. In an ideal world maybe the teacher could tweak the problem each time they see a person using a different method, to make the problem one that forces a person to use the method they are trying to teach. In the real world you usually can't give each student that kind of attention. You just have to say, "Look, I know you could solve it that way, but I need you to try to solve it this way so we can learn this method."