No one knows for sure when women started shaving their legs and underarms, but we know that ancient Egyptians pretty much shaved everything they could reach.
They were concerned about bodily cleanliness and, in a time without modem soaps and deodorants, realized that clean-shaven areas don’t offer the same welcoming atmosphere to bad-smelling bacteria that hairy ones do.
Shaving heads became an efficient way of dealing with both heat and hair lice.
From there, it wasn’t much further to simply go ahead and rid the body of the rest of its hair as well, whether on an adult or a child.
Barbers were held in high regard and often times were on the house staff of the very wealthy.
For centuries afterward, other Middle Easterners continued this practice.
Eventually, for women at least, it spread to Europe and the Americas.