Soaps aren’t fats or oils. They’re the product of *reacting* fats with alkaline substances, traditionally usually lye (sodium hydroxide).
That reaction produces a molecule with two ‘sides’. The original fat on one side repels water and attracts fats, and the extra base attached to the molecule on the other side attracts water. The combination means that soaps can help fats dissolve in water, by bonding to both the fats and the water.
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