Today, I installed an air conditioning unit in a window. I removed the windows, made the measurements, installed and secured the unit and even installed corrugated plastic above the unit. I am now an official man. Who is a little handy.
This may sound sexist or something, but really, why don't women do these kinds of tasks? Aside from the problem of lifting things, is it really that difficult for women to do? What happens if there is no man? These things just don't get done? Or is it simply a matter of women having no interest in actually doing this type of work themselves? Is it like comparing everyday housework to weekend yardwork and fix-it jobs? I really don't know.
Many women have no problems telling men how they want the work they can't do done, and scoff loudly at any and every mistake the man might make, and attack his masculinity to boot. "Aren't you a MAN? Why can't you just DO THIS?" I'd like to say that just because women can menstruate (an ability that just happens by virtue of their being women), doesn't mean that I can fix your washing machine, because that is NOT something that just happens by virtue of me being male. Just saying.

Oh really? Well I'll have you know that I fixed the rust spots on the car yesterday. Ug! Ug! Ug!
If you are attempting to be lyrical by comparing menses to "men's ease", and the huge gap betwixt, then I see your point. ;)
How about not putting all of us of the sleeker sex under some blanket characterization - some women are more than capable of getting things done in that regard. Hell, the best "handyman" I ever knew was a woman. (A very feminine and beautiful one at that - so there goes the stereotype you may or may not have had pop up).
By contrast, some of the men I've known wouldn't even know how to change a faucet washer. Which, incidentally, does not, in my view, make them any less of a man...
If that is true, then I commend you. Neither you nor the handywoman you described are at all typical, I fear.
A lot of it has to do with who is more comfortable with something. There's lots of stuff that I could do that I don't even attempt because there's someone handier than me around. That person gets to do them... and then of course accumulates experience and becomes even more handy than I am, so definitely gets the next handy job that comes up.
I was handier than my ex though, so back then I happily did all the handy stuff that needed doing. That was my job. It's not my job any more, so I don't usually even think about it.
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A long but interesting article about the meaning and appeal of masculinity by a transman. (Well, I think it's interesting.)
http://goodvibes.com/Content.aspx?id=1457&leftMenu=35&lr=y
Central quote:
"Are men good for anything at all?
I've asked as many straight women as I know about this, figuring that since they sleep with men and even live with them, they ought to know what valuable qualities they possess. It seems to be an embarrassing question. A couple of times, my het girlfriends have admitted that they like cocks or that boyfriends are useful for picking up heavy things and changing the oil in the car. One woman mentioned that her male lover was the only person who would watch "Beavis and Butthead" with her, and laugh as hard as she did. Another said that watching her boyfriend move around the apartment was like watching her big dog run through the park. There was something unselfconscious about his physicality that made her love him.
Where are the toeholds I could use to scale the wall into the castle of manliness? I like penetration, and I think I'm pretty good at it, but my dick is not a biological organ; there's no way to skirt around that deficit. I'm disabled, so I hardly ever pick up heavy things, and what I know about cars could be written on the inside of a matchbook cover in 20-point type. Physical grace is a rare and valuable experience. Most of the time I live in my head, or in a book, or in somebody else's head. My macho is in my intellect; my sharpest weapon is my tongue; my biggest muscle is my brain. I get inside other people's sexual places by understanding them, by being willing to see and accept aspects of their fantasies or needs that are usually repressed. In a world where women are supposed to feel and men are supposed to act, I stand in the middle and comprehend what both of them are doing, and why. But I remain a stranger in each of these territories."