Despite approx forty posts on this thread, (which have covered topics from; political correctness, your exploits as a teenage logger and the logging industry generally, GIs, bullying in the military, concealed weapons, flat earthers, vaccine deniers, your uncles horses and now the UK class system and migrant labourers etc etc), none have so far suggested that you have recently put on a pair of hiking boots and a rucksack and headed off (with or without a female companion) into the countryside for a lengthy walk for the sheer joy of it. I had therefore inferred (which on this side of the Atlantic is generally something different from “implying”), that hiking (which is the focus of this thread) wasn’t really your kind of thing.
Happy to be proved wrong and if you honestly think you could keep up with by 82 year old mother on a hike over pretty much any terrain (as I mentioned previously, she is slowing down a bit these days but since she was your age, despite the handicap of having two “X” chromosomes, she has stomped up and down peaks in the Nepalese, Tibetan and Bhutanese Himalayas, the Canadian Rockies, Peruvian Andes, Moroccan Atlas, Spanish Pyrenees, walked the entire coastline of Wales and much of south west England etc. etc.), then you will be doing better than most 62 year old men or indeed, women.
I suppose a carefully aimed shot by a less capable walker inflicting a minor non-lethal injury on a more capable one could even things up a bit, but from a European perspective at least, this seems a bit drastic and I am really struggling to see how guns are relevant to this discussion!
You keep telling me that I think men and women are “the same” - of course they are not any more than all men are “the same”. If the main requirements of a role are brute strength then the chances are more men than women (or possibly only men) will be able to perform the role but then you could probably train a gorilla which has ten times the strength of a man to do the job. IIRC Charlton Heston made a “documentary” about this - it didn’t end well!
There are all kinds of factors that will affect the comparative performance of two individuals hiking with heavy rucksacks. Gender may be a factor but, genetics, health, training, experience, suitability of footwear, rucksacks etc. and any number if other factors may be relevant and after a point, excessive muscle bulk becomes a hindrance rather than an asset in situations requiring endurance. As Fadcode and others have said, rather than trying to come up with a definitive formula or denying the possibility of a woman carrying more than a man, trial and error is the best approach to achieve maximum team efficiency.
Anyway, to help soothe male egos, here is a video of a young woman with a rucksack falling over!