Adult humans typically have little body hair, but abundant hair on their heads. In part this may have served as protection and insulation for the skull. But it may also have had another use.
Human infants are able to grip very powerfully. They may have needed to. Busy mothers, with work to do, could not have held their babies in their arms. The babies would have had to cling on to something. The most likely candidate is a mother's long hair, since there is little else that an infant could clutch. That hair may have been tied together at the ends to form a cradle below the mother's breasts, in which an infant fed at will.
One explanation for male facial hair may be that human mothers weaned children from breast feeding by passing them to males. Males would have had to be stronger to carry these older children. The weaned child fed from the father's mouth. Beard and moustache enabled an infant, clinging to male chest or head hair, to pull open his mouth. The weight of a child hanging from his beard may have been sufficient to pull the mouth open.
Behind this is the suggestion that humans did not spend much time actively caring for their children, simply because they did not have enough time free for it. Both males and females were too busy collecting, carrying and preparing food, and performing numerous other tasks. Infants had to fend for themselves, and clung to their mother's hair, and suckled at will, while the mother busied herself in other tasks. Adult males were similarly busy, and it was left to children to open their mouths to access chewed food. Mothers weaned children when they could no longer carry them. Fathers left older children to their own devices when they in term could not carry the weight.
One result of this relative lack of care from too-busy parents may have been high infant mortality. To the extent that infants had to fend for themselves, by clinging onto parents and feeding from them, they were in danger of falling or being underfed.