It all has to do with Newton’s laws. Especially the third one that states “for every action, there is an equal but opposite reaction.” The human body has a natural buoyancy that is not too far off from water (but is not enough to keep the head out on its own). The trick is to make movements that will result in the body (and the head) staying on top of or out of the water. Think about a paddle in the water. If you push it against the water in the direction of the skinny edge, it slices through with little resistance. If you try to push it through in the direction of the broad flat side, it seems to push back and requires much force to move.
By articulating the hands and feet in such a way that the upward strokes minimize reactive force (paddle slicing) and downward strokes maximize reactive force (paddle pushes back); the net force is that the body and head stay on the top surface and don’t sink.
If a non-swimmer falls in and just starts kicking and flailing without regard to the resultant force of their movements, they will eventually cancel out and result in the head going under when it is time to breathe.
A skilled swimmer however, develops a second nature to the reactive forces, and seems to effortlessly exude a minimum of forces that allow them to keep their head above water.
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