I think this is your point but helping spell it out. The father in this case is probably the best shot at obtaining more food for the starving family and needs energy to do so.
you've made a lot of assumptions to reach that conclusion.
for counterbalance, women burn less energy per mass on average and are less massive on average, which means they'd last longer in the search, raising the likelihood of finding food.
I'm not educated on which sex would have truly had a better chance, and not totally concerned with it. Mostly concerned with illustrating more clearly the parent posters point.
My assumption is men did more hunting and women gathering, and that in a starvation scenario, known gathering food sources would have been exhausted.
Sorry for any Paleolithic women I may have offended with my post!
for counterbalance, women burn less energy per mass on average and are less massive on average, which means they'd last longer in the search, raising the likelihood of finding food.