If you're going out with weapons to hunt with, are you also going to ignore the berries and herbs and mushrooms you find? If you're going out with baskets to bring back materials for foraging, are you going to feel stupid for not also bringing along a sling or spear when you see some small game?
Yes, statistically speaking, men have more strength and lung capacity than women. That would generally make men more effective at hunting, but that doesn't mean that women didn't hunt at all.
Oh no don't misunderstand I'm not trying to say that the whole hunter gather roles are correct. Just saying that, till now, I've always heard that's what it was. Roles. Not evolution.
Yeah, and what I'm saying is that in the nomadic hunter-gatherer days, I think it's unlikely for those roles to have emerged very strongly. We're talking about pure subsistence, and in that paradigm, you don't leave resources behind no matter who you are.
It's not until agriculture comes around that people start putting down permanent roots in one place. Now you don't have to expend effort on traveling, rebuilding shelter, moving resources. You get the luxury of storing more resources than you can carry. That's what allows people to start specializing and shifting into specific roles.
Try watching 90s sitcoms. Gender essentialism was still ok in public discourse so you hear a lot of 'because men were designed to hunt' to explain unrelated behaviour.
I think there has always been a vague yet unproven theory about it, that males generally developed to be bigger because they were more commonly in hunting roles. The kind of thing a teacher might say in high school but not really back up with anything. This could only really apply to mammals, though - in other species, eg often with birds, females are bigger. However the reason behind the size difference probably has a lot more involved in it than simply which sex did more hunting.