A lot of this boils down to simply not understanding boys' physicality in my opionion. It seems to me that the point when perfectly normal physical play stops and bullying starts is a mystery to a vast number of (predominantly female) teachers.
I'm going to go out on a limb here re gender differences, which is not something I normally subscribe to...
I have observed also, in many areas of life, that women have a lower threshold of risk, or a more sensitive perception of risk, than men. This is well recognised in business for example as a contributing factor to the lower number of female entrepreneurs.
So when the two kids come brandishing the big sticks at each other, a man is more likely (without even really analysing it as such) to think "well, the sticks aren't that heavy; they're not sharp; in relation to the size and strength of the kids they're not actually going to get seriously hurt with them - even if one does get a bit of a wallop accidentally. A woman is more likely to think "OMG boys and sticks - ahhh! put them down before somebody gets killed!"
This may just be conditioning, or it may be innate, I don't know. It may be that men, having been boys and having male bodies, just naturally understand things like how much weight a boy can handle without losing control; whether his coordination is up to keeping control of an object, etc. etc. Women don't have such a natural sense of this in relation to boys, and maybe judge it according to how it was for them as girls, or just err on the wide of caution to make sure, or something.
You see this all the time when fathers play physically with their sons, and the mothers panic about them being too rough.