There's no real answer for this question of course, but the argument I would make is that hunting is the intersection of life and death, the taking of life from the animal to give life to the hunter. Women, as birth-givers and feeders, fit well within this sphere. Not only, perhaps, the feeding and sustaining of the hunters' lives, but the rebirth of the animals to ensure continued harvests.

Only tangentially related, but check out Bakker's The Meaning of Meat and the Structure of the Odyssey. Specifically Chapter 5, "Feasting in the Land of the Dawn."

Try /r/AskAnthropology too. They're more likely to have answers you want.

Well, for one thing, the Norse gods include both a male and a female hunting deity- Skaði and Ullr. So it wasn't like hunting was seen as a purely female pursuit. It's possible that hunting was seen as a unisex pursuit as a hold-over from times when the entire tribe, men and women, needed to hunt to provide enough food. But I concur with /u/iswinterstillcoming that this is probably a better question for /r/AskAnthropology .

One argument (one that I'm not hugely convinced by) might be that there is a relationship between Indo-European religions (so everywhere outside of Africa/Americas). There is a relationship with Indo-European languages that some argues would carry on with religious ideas. There is a bit more written here under point 3 http://www.onreligion.co.uk/7-religious-ideas-worth-reflecting-on/

The argument would be that the first tribe that left Africa and populed Asia/Europe took a common culture and proto-Indo-European language with them. They would have also shared a religion. As this tribe grew and spread out across the world, the same ideas remained but were expanded on in different ways. The reason then that many hunter dieties are female is because they are all echoes of the original hunter goddess of the original tribe that left Africa so many eons ago.

It's a theory I haven't seen used in this particular context, but I have seen used to explain certain other similarities between Indo-European pantheons.

Edit: Just realised I'm posting in R/AskHistorians. I'm not too familiar with the posting rules, I usually read in this subreddit rather than contribute. In terms of references, the "Oxford Introduction to Proto-Indo-European and the Proto-Indo-European World" by Mallory and Adams is pretty the go-to for this particular theory. I note the rules say no "speculation". My answer is speculative, but in all fairness, every explantory theory I've ever read on early polytheism has been speculative - too few sources for anything but conjecture. Part of the reason I'm not a fan of the theory myself.