A couple of weeks ago I saw a story about a female chimp in a zoo who threw sticks at visitors with good accuracy. Now I see in the NY Times a story about a population of wild chimps where the females use sticks to hunt and the males respect their catches by not stealing them. Look here: http://www.nytimes.com/2015/04/15/science/hunting-chimps-offer-new-view-on-evolution.html?ref=science&_r=0
These chimps live in a mixed savannah-forest area where food is not as plentiful. The females hunt other small animals with sticks while the males go for larger ones that need catching, so speed and strength matter and no sticks involved. An anthropologist believes early Homo evolved under similar circumstances and then wonders if females originated tool use (and what? then males liked it so much they took it over?). The other part of this is that males often take food from females but leave the food caught with sticks to them.
Who knows? And what about bonobos, those friendlier apes? Food sharing and social organization are complicated matters and our burgeoning symbolic capabilities eons ago made them even more so.