In Danish/Norwegian/Swedish (man/mand), it is the same as in German (man/mann) and English (man/man). And han/ham (he/him) is the default common gender. I’ve never heard anyone making an issue out of it. Danish and English are already comparatively gender-neutral languages.
We have a winner!!! 
Would the overall task change from paragraph to paragraph? Say you were explaining how to fix a stuck photocopier, and you use “she” to explain how to open the machine, and then you have a new paragraph about extracting the stuck paper, could you use “he”, or would that be too close for comfort?
I had in mind only doing this in contexts where it is clear that we just want to refer gender neutrally. In these cases, or at least some of them, it seems like one is just bumping up against a feature of the language; no one will be confused by the gender neutral usage, but they will find the usage odd, as it just doesn’t fit the language as it stands. The idea is that one would still be able to use he and she gendered, but one would open up the possibility of using them neutrally (in the right contexts).
I should say I don’t propose this way of reforming language as a practical one, I just think the idea of going ahead and changing the usage in this way is kind of cool.
It would be just as logical to demand that everybody stop using “you guys” when referring to both sexes.
As an aside, I grew up with “y’all,” and for most of my adult life, if I heard someone say “you guys,” my brain parsed that as “you male people.” It always sounded ridiculous to hear someone say “you guys” when addressing a mixed audience, even more so with an all female audience.
And on that note, how’s about we split a word? The basic one-syllable AS word “why” really should be two words, because it can be used to ask two different and logically unrelated questions – “From what cause?” and “For what purpose?” – and using just the one word for both makes that word sound like a much, much more profound word than it really is.
Flashing on an ep from The Prisoner, where Number Six (played by a different actor this ep, the story includes a mind-transference, IIRC) crashes his agency’s (or some agency’s) near-omniscient computer just by asking it “Why?” (This was back in the 1960s, when computers understood English as English.)
Anyway, henceforth, the word “why” is purged from the language. To ask, “From what cause?” say “whee.” To ask “For what purpose?” say “whoah.” That should make conversation sound livelier! 
My favorite take on the subject:
If yours were the sex being lopped out of the language, you’d sing a different tune. I think we can afford an extra syllable in order not to deny the existence of more than half the world’s population.
The only one of those that sounds even remotely as nice is the latter. The rest are poor substitutes for the poetry and grandeur of the former. I advocate taking it back until we come up with a better alternative.
Missed the edit, The other exception being the feminist version which is just as exclusive.
Imagination in the hearts of grunts . . .
In my experience, women who do that are making a point aimed at men who think the generic “man” is fine.
I use “he or she” unless it becomes a mouthful (so I use “he or she” maybe 90% of the time). If mentioning both genders becomes inconvenient I say “men” or whatever. I’ve never had a feminist call me on it, and if one were to do it to my face I’d laugh. People can feel free to use “women.” No sweat off my back.
But that isn’t really the same thing that the OP is asking for, because it’s a term of address, as a second-person pronoun, and only carries meaning in the context of discourse. The OP wants something like the way “mankind” refers to all humans–a substantive.
When I was younger (a teenager and an early adult) I argued for the gender neutrality of man, he, etc, an effect of my Randian phase. I’ve come around to the other side but I still don’t know of any reasonable drop-in replacements. “He or she” is too cumbersome; made-up words sound silly; but I’ve generally found that prose can be rearranged to avoid such constructions without significant impact on readability.
When doing so would be awkward I use woman, she, etc., except where explicitly referring to a male person. I don’t mind being exclusive — I think the goal should be tilting the balance. Maybe the use of either gender will become so commonplace that exclusivity ceases to be an issue.
(FWIW I would never refer to an abstract employee as he in one paragraph and she in another, even were I not necessarily referring to the same employee. At least wait until some kind of section break!)
If gender inclusivity would butcher the eloquence of your otherwise movingly poetic statement, by all means, use man. But that’s no reason to try to move past the assumption of maleness in general.
Though I am a woman, I’m content to consider “man” to be gender inclusive. I think of them as two different words: one, man, means the male of my species, the other, man, is short for human and means an individual of either gender. Etymology be hanged, for me it’s a convenient fiction that separates the gender specific use of man from the gender inclusive.
Actually, nowadays, that narrative makes for a mental picture that is already half-familiar to all. And which seems to demand the invention of a whole new set of grammatical genders, personal pronouns, etc. :o
Did Rand ever make any such arguments?
The Badendyck example is not appropos. It relies on the absurdity of assuming that “he” has no gender connotations at all in any context (which is of course untrue), by using it in a context where it is absurd.
However, the same word can and sometimes does have different meanings in different contexts. For example, “man” used to (and arguably still does) mean the human animal of whatever sex, as well as a specifically male human. This isn’t all that unusual: “dog” has the same meaning for dogs - it means both the male of the species, and (more commonly) all of 'em of whatever sex.
Contrast:
Nobody goes around insisting that everyone say “dogs and bitches” when then mean “A domesticated carnivorous mammal (Canis familiaris) related to the foxes and wolves and raised in a wide variety of breeds, of either or both sexes”.
In one context, the meaning of “man” or “men” obviously is intended to be inclusive - to mean the human species (“All men are created equal”); in another context, it is obviously intended to be exclusive, to mean only males of the species (“the men’s room”). There generally isn’t a genuine problem telling the two meanings of the word apart.
The “some men wear ties and some men wear pantyhose” type example is simply deliberately mixing the two meanings up. Naturally it sounds absurd.
I think you’re all looking at this wrong. Instead of trying to come up with a new gender-neutral pronoun, I say we declare “men” gender-neutral and use “he-man” (and “he-men”) as the male-specific pronoun. This has multiple advantages:
[ul][li]Historic documents are immediately updated to be inclusive: …all men are Created equal…[/li]What man wouldn’t want to be called a he-man? I can use all the macho help I can get.[/ul]
We’ve already invented a word to replace men. Peeps. There are only two problems standing in its way: 1) Its strong association with a specific subculture, and 2) The existence of the microwavable Easter treat.
Just picture it:
[quote=“Deeg, post:38, topic:608394”]
I think you’re all looking at this wrong. Instead of trying to come up with a new gender-neutral pronoun, I say we declare “men” gender-neutral and use “he-man” (and “he-men”) as the male-specific pronoun. This has multiple advantages:
[ul][li]Historic documents are immediately updated to be inclusive: …all men are Created equal…[/li][li]What man wouldn’t want to be called a he-man? I can use all the macho help I can get.[/ul][/li][/QUOTE]
Too homoerotic.
By the power of Grayskull…