It only floats on water because it has nowhere else to go. Can’t go down, can’t go up, and going to the side is just more water. So all the oil just huddles together. But if it’s already on your hand, it will happily stick to it, because your skin doesn’t repel oil.
As to why water doesn’t displace it away, water doesn’t just *displace* oil. When you wash your hands, what water is actually doing is sticking to things like dirt and grime. Then it drags it away down the sink as they’re all washed away. Water doesn’t really want to stick to oil, and so we use soap, which is like a mediator between oil and water. Water sticks to soap, soap sticks to oil, and the 3 friends get washed down the sink all as one.
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