One of the most common mistakes less experienced dancers make is to try to lead and follow with their hands and arms. Men in particular, try to lead like they are steering a car - with their hands. Leading with the hands and arms tends to compromise the integrity of the two-headed four-legged animal.
In the past, it was deliberately taught to lead with the fingertips, the heel of the hand, etc. Unfortunately, there are still some instructors that have not progressed in their techniques and still teach it. It is not wrong; there is just a better way. Better doesn't necessarily mean easier, so these types of things seem to linger on.
Dancing evolves over time and an instructor should not be afraid to change. Some instructors think that if they change what they are teaching, the students will think they were teaching it wrong. There is no wrong in dancing, just better. An instructor should always be looking for better ways for their students.
You should think of not having any hands or arms. They should be thought of as part of the body of the two-headed four-legged animal. The hands and arms are just a mechanism to connect the two halves. They form the frame that defines the relationship between the two partners that is the single entity - the "two-headed four-legged animal". The frame (composed of the arms, hands and the backs across the shoulders) should not be moving independently of the body (an exception would be lifting the hand/arm to indicate an under arm turn).
The hands and arms of the frame should be treated as if they were made of cartilage, not muscle and bone. If this were true, the frame could not move independently of the body. The frame would be flexible, pliable, stable, constant, strong, and maintain the proper relationship to the other half (partner).
In reality, the left side of the frame (from leaders point of view) uses some arm muscles. Leading into "promenade position" and "open breaks" would be some examples.
In Rhythm dances such as "Cha Cha", "Rumba", "West Coast Swing" etc., there are a lot of one-hand connections. The above is still true. For example in a "W.C. Swing" "Left Side Pass", the body leads the lady down the slot not the arm. The arm just happens to be attached to the body. The arm by itself does not have enough mass to gracefully lead the lady. The goal of W.C. Swing is to be as smooth and continuous as possible. Using the body (because of it's mass) allows you to achieve this goal. Trying to lead with just the arm will result in jerky and erratic results.
The same is true from a follower's point of view. The cartilage like arms forms a "closed" or "open position" frame that maintains the proper physical relationship of the partnership. In the example of the "Left Side Pass", the follower should feel like her body is moving down the slot. She should not feel she is chasing her hand down the slot. When the frame/lead is correct, the lady should feel like she is participating in the lead instead of responding to the lead.
The frame/connection of the partners to create the two-headed four-legged animal is a shared responsibility. Both sides of the partnership must participate equally to create the oneness of the single entity.
The frame unites the two sides to create the oneness we are all trying to achieve. We truly must feel that we really do have two heads and four legs. After a while two heads and four legs feels normal and you will use them as if they were your very own.