Soap is a special compound.
Oil and Water normally cannot mix. Oil is a non-polar molecule. Water is a polar molecule. Polar and non-polar cannot mix. Enter Soap.
Through a chemical process, soap is a molecule that has a polar component to it as well as a non-polar component of it. So you rub on the soap and the non-polar portion of the soap binds with the oils on your skin and then when you rinse with water, the polar portion of soap is caught up by the water and washed away, taking the oils with it. This is how soap works.
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