For clarification, the "men on the internet" I refer to with this:
"Is this the thing where the men on the internet gleefully say "Ha! Women said they wanted to be equal, that means I can punch them in the face!" which is a weird thing to say whichever way you look at it"
They are not talking about in self defence. They are saying, ha, now I can walk up to women and punch them in the face. Take that, feminists!
Maybe you haven't come across them 
The response of:
"Why? I've always found it interesting how willing women are to hit men* and how utterly surprised they are on the rare occasions they are struck back. "
Doesn't chime with me either. I've been punched in the face on the street by a strange man (I was waiting at a bus stop, had a suspected broken jaw), had a man pour beer over my head, and of been otherwise assaulted stacks of times in a non violent but sexual manner.
I've never been attacked by a woman and I've never seen a man be attacked by a woman. I have seen men and women drunkenly fight, including a man trying to put his girlfriends head through a window, seen a man glassed (by another man) and been present at plenty of impromptu fights in pubs and indeed outside them with police vans racing up and down the road. So I don't think it's a question of being sheltered....
Why are so many women so keen to say that women are just as violent and dangerous as men, despite all evidence to the contrary? There's the size thing as well. No-one should hit anyone, however if I hit my husband I'd not damage him much, if he hit me I'd likely be killed. Us punching each other is not "equality" it's a terrible idea as no-one should hit anyone, and it's a very uneven match.