When we watch competent people dance what we are observing is them demonstrating a level of skill that they already have. This skill was acquired through a process of training which was most likely progressive, that is, involved a series of steps whereby they started off with no skill and then progressively acquired the high level skill that allows them to dance skilfully.
This is important because many people seem not to realise that what you do in the process of training is going to be very different from what one sees when dancers demonstrate skill that is the result of a process of training. Many (perhaps most) people see skilful dancers do a certain pattern of steps or some movement and they want to immediately learn how to do that specific pattern or movement.
They want to learn that without apparently taking into consideration that they are not at the level to be able to execute that pattern or movement simply because executing it would require a level of skill that they do not yet possess. I think that the idea that many people have is that learning the pattern of steps and movement just requires a lot of practice of those steps or that movement in order to acquire the skill.
This, however, is a major confusion about the relationship between the process of training and demonstration of a skill acquired through that training. The pattern of steps or the movement is not the skill itself but a demonstration of movement skills that are distinct from the pattern, and that are presupposed in executing that pattern skillfully. By analogy, one does not learn to drive fast by driving fast. One first has to learn to drive slowly and then progressively faster. You do not learn to beat champion chess players by playing them from the start. You have to go through baby steps.
The problem is that in many (perhaps most) areas of expertise the skill required to perform an action is not acquired by performing that action repeatedly but rather by a completely different and separate process. The teachers typically know the process that can get the student from his current level of skill to the level required to perform the action that the student desires.
Whether the student undertakes the correct training depends on both the teacher and the student. The student wants to learn to perform the action and the teacher can bamboozle the student by teaching what the student thinks he wants. Alternatively, the teacher can tell the student that the process requires doing something else to get to the desired destination. It is then up to the student to trust the teacher to show the right path. The image of the Karate Kid washing the car is the correct view of the situation.
This applies in many areas of expertise where the skill demonstrated and the training required to attain that skill are quite different. Many sports require physical strength that cannot be achieved by doing that sport itself but by lifting weights or some other sort of more basic training. In music, learning to play long sequences of fast notes typically requires the patient practice of short sequences of notes at an excruciatingly slow pace to train the muscle memory in the hands.
If you just think about it, tango teachers would not be so generous handing out their spectacular stage choreography if they thought that the students could actually effectively execute it because then they would be creating unwanted competition. They know too well that attempting to perform these sequences sets the students back more than anything else. Also, many people naïvely think that if they practice these sequences they will be able to set up as teachers themselves. They often find that they never really get anywhere close to the level they expect. They were too impatient.
Like it or not, the reality is that the fast way to mastery is through slow practice: to execute a complex set of movements fast one has to first practice executing simple movements in a slow and focused way. These are not going to be the eye-catching choreographed sequences that one sees performed by champion dancers who then teach them in workshops. Trying to execute these complex patterns merely results in the acquisition of inefficient movement habits.
Performance of sequences is the demonstration of a skill that was acquired through training, and training is not merely the practicing of the performance of these skills but a completely separate process which is progressive and culminates on the skill demonstrated.
Thomas M. Sterner The Practicing Mind: Developing Focus and Discipline in Your Life, Master Any Skill or Challenge by Learning to Love the Process [Amazon]