Personally, I think "every individual has to know how to do all the same things (or else they aren't really a member of the species and must be eradicated)" is for insects, and "having lots of options for how to live" is for human beings. Also I think "being able to work in groups so that different people can contribute their different talents and don't need to do things they're not good at or are physically incapable of doing" is for human beings. (It seems to work pretty well for some insects too.)
The only sense in which I agree with the spirit of the list, if not the letter, is that I think trying to learn and do a variety of things is good for most individual humans, and I think refusing to do or learn something because it's beneath you is not an attitude that helps most individual humans be better people.
* change a diaper -- I haven't done this, as it happens, although I've cleaned shit off of plenty of things and I think that this would probably translate to being able to change a diaper.
* plan an invasion -- Of what? I don't see the slightest utility for this, for most people. I haven't done this. I don't play war games either. I have read many books and watched many movies that involved planning invasions though. Some of them probably had good theories for how to do it well. So I guess I could take a stab at it.
* butcher a hog -- I haven't done this. I'd need to do it with some kind of instructions in hand, and the proper tools, and it would probably be pretty difficult for me given my physical limitations, but I think I could do it.
* conn a ship -- I've steered boats around lakes - rowboats, canoes, sailboats, and motorboats. I haven't done the same with ships and haven't done it on the ocean, and I haven't charted courses for watergoing vessels. I think that would take quite a lot of study because I don't know very much about ships. I'm not very confident about my navigation abilities when I don't have human landmarks and maps of same to plot a route by, so I don't know if I could learn that. No doubt I could learn to do it if I had a GPS to rely on though. Frankly, I have no idea why it's important for a human to know how to conn a ship. Most ships require entire crews that are quite specialized and many humans don't have any particular need to travel by ship. I think RAH/LL were just showing off here.
* design a building -- I can draw a floor plan, and I know a little bit about framing a building and so forth (and know where I could find out more) but unless the building were no more complex than a door, four walls, and a roof, I think I'd need to study architecture to learn how to design it properly. I'm sure I could learn architecture, but I really don't see why detailed architectural knowledge is something all humans should know. If this had said "build a shelter," I might agree with it more; I guess it's silly of me given how little wilderness is left on the planet, but I think a little wilderness survival knowledge is a good thing to have.
* write a sonnet -- what janetmiles said: I am sure I could come up with something that complies with the form. Would it be any good? Probably not. Actually I could probably write a decent sonnet if I practiced hard enough, but rhyming structured poetry is not my forte. I would change this to "Write a haiku." Writing a haiku using all the rules (not just 5-7-5 but the rules about season words and so forth) is devastatingly simple and devastatingly difficult at the same time and it makes you think in good ways.
* balance accounts -- Yes, and I think most people do need to know how to do this.
* build a wall -- I haven't done this but I could learn how; it would be difficult for me to actually do it because of my physical limitations.
* set a bone -- I haven't done this but I could learn how and do it for a simple fracture.
* comfort the dying -- I've tried to do this, I haven't ever found out if my attempts were actually comforting. And I think it's a good thing for people to know how to do, but I think it's more important for people to learn how to grieve - that is, how to address the universal fact of dying.
* take orders -- I've carried out instructions. To me "orders" are something I have to follow without thinking, and I believe it would be impossible for me to do things without thinking.
* give orders -- I've given instructions and had them carried out.
* cooperate -- I have done this and can do this, although I'm less cooperative than some people.
* act alone -- I have done this and can do this. By the way, for this item and the previous three I would also add "Know when to...[take/give orders, cooperate/act alone]." I think that is more difficult than knowing how.
* solve equations -- I have and can. For equations that are more complex than basic arithemetic I might need to refresh my memory about how they work. My brain doesn't retain mathematical knowledge all that well.
* analyze a new problem -- Yes, depending on the problem. This is awfully vague.
* pitch manure -- I can shovel snow; is that close enough? Being able to handle shit without getting completely squeamed is probably an important ability; I don't think pitching manure per se is an essential skill. A lot of people don't get anywhere near a pile of manure any more.
* cook a tasty meal -- Yes, and it's definitely a good skill for most folks to have.
* fight efficiently -- Verbal fighting yes. Physical fighting no, unless "efficiently" means "avoiding physical fighting."
* die gallantly -- I don't see why this is something everyone has to do. We all die whether we know how to or not. Furthermore, to die gallantly implies dying in the service of some cause, probably violently, rather than dying asleep in one's bed. Personally I think I'd prefer the latter.
Finally, in some of the commentaries I've seen people add to the list. The best thing I saw added was something along the lines of "Spot a faulty argument." I like that because to really do it well one has to learn things about logic, rhetoric, and statistics. I think most people would benefit from learning about those things.
I think I might also add "Recognize/defuse an escalating spiral of aggression/fear." That's one of the most useful skills I've ever learned.