Why does a swimmer use his hands to push water behind in order to swim forward?

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Solution

Newton's Third Law of Motion:
Newton's Third Law of Motion states that when a force is exerted by a body on another body(action), they experience an equal and opposite reaction.
So, According to Newton's third law of motion, there is an equal and opposing reaction for every action.
So, if he pushes the water backward, he will be allowed to move forward according to the law.
Hence the swimmer pushes the water backward with his hands in order to swim forward.

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