When we watch competent people dance what we are observing is them demonstrating a 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 in a complex way skillfully.
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 their skill that is the result of the training. They see skillful 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 themselves at the level to be able to execute that pattern or movement, because executing it would be a matter of demonstrating a level of skill that they do not yet have. I think that the reasoning is that learning the pattern of steps and movement then 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 training and demonstration of a skill. The pattern of steps or the movement is not the skill itself, but a demonstration of movement skills that are distinct from the pattern. 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 areas of expertise, the skill required to perform an action is not acquired by performing that action repeatedly, but rather by a completely different process. The teacher knows 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 pupil: the pupil wants to learn to perform the action and the teacher can bamboozle the pupil by teaching what the pupil thinks he wants. Alternatively, the teacher can tell the pupil that the process requires doing something else to get to the desired destination. It’s then up to the pupil 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 training. In music, learning to play long sequences of notes fast requires patient practice of short sequences at an excruciatingly slow pace.
Tango teachers would not be so generous with handing out their stage choreography if they thought that the students could effectively execute them, 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. Conversely, many students naively believe that if they master the sequence they will be able to set up as teachers themselves. They are then surprised that they never really get anywhere close to the level they would 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. Trying to execute these complex patterns merely results in the acquisition of poor 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.