This isn't a traditional male activity, per se, but the way I do it isn't the way most women do it. I do long hikes in the desert and mountains, alone. People are always telling me I'm crazy, or that I should hike "in a group".
But I hate groups, especially in the wilderness. People also ask me if it's safe from predators of the two-legged kind. I tell them over the years I've never had a problem with anyone out on the trails, despite encountering men hiking alone all the time. There's a comraderie among wilderness people. The men I run into out there, after their initial surprise at seeing a woman hiking alone, are universally cool with it. I get along fine with them.
In contrast, I have more than once had trouble in organized campgrounds, and as a result I refuse to camp in them. One night many years ago a guy slipped into my tent in a Forest Service campground in California and wouldn't leave. I should have sex with him, he said, because "no one will ever know". Now that's some kind of logic for you, eh?
Well, I don't know if he was planning on forcing me or what, but when I hike I carry a gleaming buck knife with a blade as long as my forearm, and I keep it at my side in my tent. I brandished that blade in the guy's face and told him if he didn't get out of my tent, he was losing his balls. The look on his face was priceless. He wasn't quite sure if he believed I'd really do it (I wasn't sure myself, to be honest). But he decided he didn't want to take the chance, and left.
Since that night, I camp instead out by myself, away from campgrounds.