Let me try a different way of explaining the issue.
Much of the time in the swing dances are weight is not balanced at a point between our feet, but instead must leave the position of stability over the standing foot before the receving foot is there to receive it.
To take one of the harder examples, imagine you are dancing waltz and have risen to foot closure, so that you are about to lower and divide your legs into a new step. A beginner will lower with their body balanced over their standing foot, swing the moving leg forward into an obvious heel lead, and then shift their body between their feet.
A coordinated dancer will do something a bit different. Their body will remain relatively stationary until their standing heel touches down on the floor. But as their knee starts to bend to continue the lowering, something changes. Instead of letting the knee bend forward of the body, the body rides forward on top of the knee, such that the front of the thigh stays almost vertical over the kneecap. Try this and you will find that at first you can maintain static balance (and thus dance the action arbitrarily slowly) by using the toes of your standing foot to support you. But soon the point of your static balance moves past your toes, and you must either fall forward or distort your body position to regain balance. Or do what we actually do in dancing, which is to speed the motion of the body forwards as it falls beyond our balance, so that a stumble becomes a gracefull swing. Unlike the beginner, this dancer will keep the moving leg behind during the early part of this process - after all, it weighs quite a bit, and having it forward of you will only make your fall into the step sooner. But at the right instant the moving leg begins it's delayed swing forward under the moving body, develops from toe drag to heel lead so fast you might not even see it, and catches the weight of the body as it arrives and swings through (and probably up) into the next figure.
Many teachers start beginner students with the goal of simply building awareness of how one is dancing, even if most of the details are wrong. Awareness is certainly a necessity, but practicing incorrect techniques may require a lot of difficult work in the future to counteract the resulting limiting habits. This still seems to work as an education model, because most of the students won't advance to the point where they are aware of the limitations those beginner habits create (though if they are otherwise doing well, it will be obvious to a skilled observer). Unfortuntely, quite a few teacher's own dancing is little more than a precise execution of beginner methods - perhaps stretched to a usage at a moderate level of competition in the past, but not possessing the fundamental details which advanced dancers use to execute basic figures.