This is because you have tacit knowledge of where the tip of your nose is and how you must move your arm to touch it. In the exercise, moreover, you were consciously focusing on your tacit knowledge. Normally we do not concentrate so deliberately on the physical motions we make. If we did, we would never get anything done, because our conscious minds are hopelessly inefficient information processors compared to our unconscious minds. While you were deliberately and laboriously focusing on the movement of your arm, your brain was rapidly and efficiently dealing with an enormous amount of other information to keep track of all your bodily functions.
Conscious thought is thus energy-intensive and inefficient.
On the other hand it is very flexible. It can be switched in a fraction of a second to concentrate our attention on our heads or our toes, on listening carefully or on reflective thinking. If you really had to explain in writing how you did in detail, you would have to spend days not seconds, and you still would not be able to do it properly. This is because we are very good at doing things tacitly, so good that we can express only a fraction of it in words. A much better way is to show how you do.