Tl;dr an undergraduate paper last year claiming females hunt just as often as males got picked up by the media and amplified before it was discovered their analysis was deeply flawed and unreliable. Here several anthropologists present a very gracious rebuttal.
I fins it hard to believe that humans did not realize what we know today where you pretty much gather, set traps, and do hunting of opportunity when alone or in small groups with some formal group hunting that pretty much uses anyone available. I could see more gender division happening with farming and domestication.
If I can quote the authors:
There could be an advantage for groups that had males do the riskier jobs because the cost of losing a male is much less than a female in terms of maintaining population.
This is pure speculation on my part though, I have no education here and no idea what I’m talking about.