Rabbits have plantar hair, hair growing on the equivalent of human palm. It turned out that the gene DKK2 is responsible for preventing follicles from developing on the palm. By knocking down DKK2, scientists have been able to make mouse to grow plantar hair.

As for why primates loss their plantar hair, it is likely that hairless palm affords more advantage for tree-dwelling.

Why don't we have fur over all our bodies? There was a popular book long ago, about us, called "The Naked Ape".

Think about the Hint in your question.
Think about how sensitive our finger tips are to touch.
Think about how the hairy parts of our bodies never touch anything in the same way as our fingertips. But the hairy parts can sometimes sense something even before it touches our skin. Try this, with a piece of paper that just touches the ends of your arm hairs.

My guinea pigs have a long whisker near each eye, and, if I touch the end of one of the whiskers, they turn their head in that direction.